Introduction to Maximal Function
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Maximal Function sentence examples within conditional quadratic variation
We obtain the exponential integrability of the maximal function, the quadratic variation and the conditional quadratic variation of bounded martingales and exponential integrable martingales.
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In this article, we introduce the martingale Musielak-Orlicz Hardy spaces \(H_\varphi ^*\left({\rm{\Omega}} \right)\), Pϕ(Ω), \(H_\varphi ^S\left({\rm{\Omega}} \right)\), Qϕ(Ω) and \(H_\varphi ^s\left({\rm{\Omega}} \right)\), respectively, via the maximal function, the quadratic variation and the conditional quadratic variation of martingales.
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Maximal Function sentence examples within Littlewood Maximal Function
Explicit upper and lower bounds for the two-dimensional discrete Hardy–Littlewood maximal functions from $$\ell ^{1}({\mathbb {Z}}^{2}) $$
to the space of functions of bounded variation $$\mathrm {BV}({\mathbb {Z}}^{2}) $$
are obtained.
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We obtain bounds in full range of exponents for the Hardy-Littlewood maximal function on spaces defined via Choquet integrals associated to Bessel or Riesz capacities.
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Maximal Function sentence examples within Fractional Maximal Function
An optimal global Calderon-Zygmund type estimate for such problems is obtained by using mapping property of the fractional maximal function of the measure.
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We will also prove the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator (fractional B B -maximal function) on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces.
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Maximal Function sentence examples within Type Maximal Function
Maximal Function sentence examples within Grand Maximal Function
Let H p(·) A (R n) be the variable anisotropic Hardy space defined via the non-tangential grand maximal function.
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In this article, the author introduces the “geometrical” variable Hardy spaces H p(·) r (Ω) and H p(·) z (Ω) on Ω, and then obtains the grand maximal function characterizations of H p(·) r (Ω) and H p(·) z (Ω) when Ω is a strongly Lipschitz domain of Rn.
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Maximal Function sentence examples within Sharp Maximal Function
The proof of the latter result is based on the appropriate estimates for the sharp maximal function which are consequence of the sharp variant of the Rubio de Franca’s extrapolation result for variable exponent Lebesgue spaces.
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In this article, we discuss the connections of function of bounded mean oscillations with weight functions, sharp maximal functions and Carleson measure.
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Maximal Function sentence examples within Spherical Maximal Function
In this work, the boundedness of the spherical maximal function, the mapping properties of the fractional spherical maximal functions, the variation and oscillation inequalities of Riesz transforms on Herz spaces have been established.
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Firstly, we obtain $L^p\times L^q \to L^r$ estimates for the bilinear spherical maximal function on the optimal range.
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Maximal Function sentence examples within Achieve Maximal Function
Success depends on a variety of factors: location and severity of the injury, age and physical condition of the patient, therapeutical approach, … Therefore, it is important to search for the best possible means to achieve maximal functional recovery.
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Patients and providers would benefit from a more complete understanding of the rate of improvement, the average length of time to achieve maximal function and minimal pain, and whether there is a greater decline in function or an increase in pain over time following TAA compared with AA.
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Maximal Function sentence examples within Radial Maximal Function
In this article, the authors introduce the weak Hardy-type space $WH_X({\mathbb R}^n)$, associated with $X$, via the radial maximal function.
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Let $$\overrightarrow a \,: = \,\left( {{a_1}, \ldots,{a_n}} \right) \in {\left[ {1,\infty } \right)^n},\,\overrightarrow {p\,}: = \left( {{p_1}, \ldots,{p_n}} \right) \in {\left( {0,1} \right]^n},H_{\overrightarrow a }^{\overrightarrow p }\left( {{\mathbb{R}^n}} \right)$$
be the anisotropic mixed-norm Hardy space associated with $$\overrightarrow a $$
defined via the radial maximal function, and let f belong to the Hardy space $$H_{\overrightarrow a }^{\overrightarrow p }\left( {{\mathbb{R}^n}} \right)$$.
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Maximal Function sentence examples within Strong Maximal Function
In 1935, Besicovitch proved a remarkable theorem indicating that an integrable function f on R is strongly differentiable if and only if its associated strong maximal function MSf is finite a.
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In this paper, the weighted grand Lebesgue spaces with mixed-norms are introduced and boundedness criteria in these spaces of strong maximal functions and Riesz transforms are presented.
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Maximal Function sentence examples within Rademacher Maximal Function
Maximal Function sentence examples within Centered Maximal Function
In this paper, building upon ideas of Naor and Tao [13] and continuing the study initiated in [16] by the authors and Safe, sufficient conditions are provided for weighted weak type and strong type (p, p) estimates with p > 1 for the centered maximal function on the infinite rooted k-ary tree to hold.
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For all $$p>1$$ p > 1 and all centrally symmetric convex bodies, $$K\subset {\mathbb {R}}^d$$ K ⊂ R d defined Mf as the centered maximal function associated to K.
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Maximal Function sentence examples within Kakeya Maximal Function
Maximal Function sentence examples within Multilinear Maximal Function
In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space.
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After defining the spaces, we investigate the multilinear maximal function, the multilinear fractional integral operator and the multilinear Calderón-Zygmund operators, respectively, from multi-Morrey spaces to Morrey spaces.
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Maximal Function sentence examples within maximal function estimate
Secondly, we show that the maximal function estimate related to one Schrödinger equation can fail with data in Ĥ p 2 (R)(s < 1 p ).
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We establish the corresponding sharp maximal function estimates and obtain the weighted Coifman type inequalities, weighted Lp(wp)→Lq(wq)$L^{p}(w^{p}) \rightarrow L^{q}(w^{q})$ estimates, and the weighted endpoint estimates for such commutators.
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Maximal Function sentence examples within maximal function associated
In this paper we establish weighted estimates for the maximal function associated with the finite type curve in the plane R 2.
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We will also prove the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator (fractional B B -maximal function) on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces.
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Maximal Function sentence examples within maximal function inequality
In this paper, we establish sharp maximal function inequalities for the Toeplitz-type operator associated with the singular integral operator with a variable Calderon-Zygmund kernel.
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In this paper, we establish the weighted sharp maximal function inequalities for the Toeplitz type operator associated to the singular integral operator with variable Calderon- Zygmund kernel.
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Maximal Function sentence examples within maximal function characterization
In this article, the author introduces the “geometrical” variable Hardy spaces H p(·) r (Ω) and H p(·) z (Ω) on Ω, and then obtains the grand maximal function characterizations of H p(·) r (Ω) and H p(·) z (Ω) when Ω is a strongly Lipschitz domain of Rn.
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In this article, via the non-tangential grand maximal function, the authors first introduce the anisotropic mixed-norm Hardy spaces $H_A^{\vec{p}}(\mathbb{R}^n)$ associated with $A$ and then establish their radial or non-tangential maximal function characterizations.
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In this paper, we establish $$L^{p}$$Lp estimates for certain class of maximal functions on product domains with rough kernels in $${L^{q}}(\mathbf S ^{n-1}\times \mathbf S ^{m-1})\,(n,m\ge 2).
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In this paper we define variable exponent LorentzSobolev spaces and prove the boundedness of maximal function in these spaces.
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A characterization of -maximal functions is also shown.
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Supramaximal functional-based resection seems to prevent DLGG malignant transformation.
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Implications for rehabilitation Coronary artery bypass grafting is a treatment aimed to improve expectancy of life and prevent disability due to the disease progression; The use of pre-operative submaximal functional capacity test enabled the identification of patients with high risk of complications, where patients with delayed oxygen uptake kinetics exhibited worse short-term outcomes; Our findings suggest the importance of the rehabilitation in the pre-operative in order to “pre-habilitate” the patients to the surgical procedure; Faster oxygen uptake on-kinetics could be achieved by improving the oxidative capacity of muscles and cardiovascular conditioning through rehabilitation, adding better results following cardiac surgery.
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Moreover, it is well-known that for the particular case $\Phi(t)=t(1+\log^+t)^m$ with $m\in\mathbb{N}$ these maximal functions control, in some sense, certain operatos in Harmonic Analysis.
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In addition, a new inequality that involves the vector inequality of the maximal function of Hardy-Littlewood is prov.
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Our method of proof combines the contraction principle applied to the associated integral equation together with interpolations of some smoothing effects (Kato’s smoothing effects, Strichartz estimate and estimates for the maximal function) for phase localized functions associated to the linear dispersive part of the equation, and a fractional vector-valued Leibniz’s rule derived by Molinet and Ribaud in (2004).
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Importantly, the CD8 binding-independent vaccine-induced CD8 T-cells displayed enhanced functional avidity, reaching a plateau of maximal function.
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Neurological and functional recovery occurs mainly within the first 6 weeks after onset of stroke, but the process continues for several months, with maximal functional recovery usually achieved within 6 months.
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Rehabilitation treatment should start from the intensive care unit, and continues until the patient reaches a plateau of maximal functional improvement.
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Moreover, the L2$L^{2}$-bounds of the maximal functions related to the above integrals are also established.
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The maximal function 𝒜*f = supN|𝒜N f | satisfies (p, p) sparse bounds for all 1 < p < 2.
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For a set U of positive numbers consider the maximal function $${\mathcal {H}}^U \,f= \sup \{|H^{(u)}\, f|: u\in U\}$$ H U f = sup { | H ( u ) f | : u ∈ U }.
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We build a connection to cut-generating functions in the Gomory–Johnson and related models, complete the characterization of maximal functions, and prove analogues of the Gomory–Johnson 2-slope theorem and the Basu–Hildebrand–Molinaro approximation theorem.
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Aging is a universal asynchronic and heterogeneous process which induces a series of changes in the organisms through time, characterized by the attenuation of functional performance compared to the maximal functional strength reached around the second decade of life.
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Because multiple mechanisms contribute to the functional loss after SCI, combining the most promising approaches that target different pathophysiological and molecular mechanisms should exhibit synergistic actions for maximal functional restoration.
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Operative management goals to reach a stable ankle with maximal function, decrease the risk of post-traumatic degenerative changes, and diminish the risk of complication.
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The main aim of this article is to demonstrate the difference of the trigonometric and the Walsh system with respect to the behaviour of the maximal function of the Fejér kernels.
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Moreover, in rest of this paper, we also give the proof of the boundedness property of maximal function on Lorentz spaces and also the global gradient estimates of solution.
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Conclusions The measured improvements in gait kinematics, spatiotemporal variables, gait symmetry, and CHAMP scores as a result of the IDEO show significant functional benefit, making it a useful adjuvant therapy in patients who are motivated to achieve the maximal functional outcome after this devastating injury.
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A mean percentage of maximal function was 88.
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We also extend a result on boundedness, in mixed norm, of a maximal function-type operator from the case of the unit disc and the unit ball to general domains in ℝn.
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Early microsurgical intervention for properly selected patients will result in maximal functional benefit that couldn’t be otherwise obtained.
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Let us denoted the maximal function satisfying the conditions above by $\psi_0$.
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Maximal functions are among the most important operators in harmonic analysis and are some of those that are most studied.
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In this note we establish certain weighted estimates for a class of maximal functions with rough kernels along “polynomial curves” on.
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DISCUSSION
In cases of accidental intracranial administration of parenteral nutrition, we recommend that aggressive therapy be pursued to minimize the risks of developing comorbidities such as meningitis and to allow for maximal functional recovery.
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