Introduction to Exponent Morrey

What is/are Exponent Morrey?

Exponent Morrey - In this paper, we study the boundedness of the operators T and $$T_{\vec {b}}$$ on generalized weighted variable exponent Morrey spaces $$M^{p(\cdot ),\varphi }(w)$$ with the weight function w belonging to variable Muckenhoupt’s class $$A_{p(\cdot )}({{\mathbb {R}}^n})$$. ^[1] In this paper, we study the boundedness of multilinear commutators of Calderon–Zygmund operators $$T_{\mathbf {b}}$$ on generalized variable exponent Morrey spaces $$M^{p(\cdot ), \varphi }$$. ^[2] We study fractional potential of variable order on a bounded quasi-metric measure space $$(X,d,\mu )$$ as acting from variable exponent Morrey space $$ L ^{p(\cdot ), \lambda (\cdot )} (X) $$ to variable exponent Campanato space $$ \mathscr {L } ^{p(\cdot ), \lambda (\cdot )} (X) $$. ^[3] For a class of sublinear operators, we find conditions on the variable exponent Morrey-type space Lp(⋅),q,ω(⋅,⋅)(Rn) ensuring the boundedness in this space. ^[4] We prove the boundedness of the fractional integration operator of variable order α ( x ) in the limiting Sobolev case α ( x ) p ( x ) = n − λ ( x ) from variable exponent Morrey spaces L p ⋅ , λ ⋅ Ω into BMO ( Ω ), where Ω is a bounded open set. ^[5] In this paper, we study various embedding theorems on variable-exponent Morrey spaces. ^[6] We continue the study of the variable exponent Morreyfied Triebel–Lizorkin spaces introduced in a previous paper. ^[7]

Variable Exponent Morrey

In this paper, we study the boundedness of the operators T and $$T_{\vec {b}}$$ on generalized weighted variable exponent Morrey spaces $$M^{p(\cdot ),\varphi }(w)$$ with the weight function w belonging to variable Muckenhoupt’s class $$A_{p(\cdot )}({{\mathbb {R}}^n})$$. ^[1] In this paper, we study the boundedness of multilinear commutators of Calderon–Zygmund operators $$T_{\mathbf {b}}$$ on generalized variable exponent Morrey spaces $$M^{p(\cdot ), \varphi }$$. ^[2] We study fractional potential of variable order on a bounded quasi-metric measure space $$(X,d,\mu )$$ as acting from variable exponent Morrey space $$ L ^{p(\cdot ), \lambda (\cdot )} (X) $$ to variable exponent Campanato space $$ \mathscr {L } ^{p(\cdot ), \lambda (\cdot )} (X) $$. ^[3] For a class of sublinear operators, we find conditions on the variable exponent Morrey-type space Lp(⋅),q,ω(⋅,⋅)(Rn) ensuring the boundedness in this space. ^[4] We prove the boundedness of the fractional integration operator of variable order α ( x ) in the limiting Sobolev case α ( x ) p ( x ) = n − λ ( x ) from variable exponent Morrey spaces L p ⋅ , λ ⋅ Ω into BMO ( Ω ), where Ω is a bounded open set. ^[5] We continue the study of the variable exponent Morreyfied Triebel–Lizorkin spaces introduced in a previous paper. ^[6]

exponent morrey space

In this paper, we study the boundedness of the operators T and $$T_{\vec {b}}$$ on generalized weighted variable exponent Morrey spaces $$M^{p(\cdot ),\varphi }(w)$$ with the weight function w belonging to variable Muckenhoupt’s class $$A_{p(\cdot )}({{\mathbb {R}}^n})$$. ^[1] In this paper, we study the boundedness of multilinear commutators of Calderon–Zygmund operators $$T_{\mathbf {b}}$$ on generalized variable exponent Morrey spaces $$M^{p(\cdot ), \varphi }$$. ^[2] We study fractional potential of variable order on a bounded quasi-metric measure space $$(X,d,\mu )$$ as acting from variable exponent Morrey space $$ L ^{p(\cdot ), \lambda (\cdot )} (X) $$ to variable exponent Campanato space $$ \mathscr {L } ^{p(\cdot ), \lambda (\cdot )} (X) $$. ^[3] We prove the boundedness of the fractional integration operator of variable order α ( x ) in the limiting Sobolev case α ( x ) p ( x ) = n − λ ( x ) from variable exponent Morrey spaces L p ⋅ , λ ⋅ Ω into BMO ( Ω ), where Ω is a bounded open set. ^[4] In this paper, we study various embedding theorems on variable-exponent Morrey spaces. ^[5]