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• W4386389681 abstract "Abstract In this article, we introduce anisotropic mixed-norm Herz spaces <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msubsup> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mo>˙</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent=true> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant=double-struck>R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {dot{K}}_{overrightarrow{q},overrightarrow{a}}^{alpha ,p}left({{mathbb{R}}}^{n}) and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msubsup> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent=true> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant=double-struck>R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {K}_{overrightarrow{q},overrightarrow{a}}^{alpha ,p}left({{mathbb{R}}}^{n}) and investigate some basic properties of those spaces. Furthermore, we establish the Rubio de Francia extrapolation theory, which resolves the boundedness problems of Calderón-Zygmund operators and fractional integral operator and their commutators, on spaces <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msubsup> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mo>˙</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent=true> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant=double-struck>R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {dot{K}}_{overrightarrow{q},overrightarrow{a}}^{alpha ,p}left({{mathbb{R}}}^{n}) and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msubsup> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent=true> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant=double-struck>R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {K}_{overrightarrow{q},overrightarrow{a}}^{alpha ,p}left({{mathbb{R}}}^{n}) . Especially, the Littlewood-Paley characterizations of anisotropic mixed-norm Herz spaces are also gained. As the generalization of anisotropic mixed-norm Herz spaces, we introduce anisotropic mixed-norm Herz-Hardy spaces <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>H</m:mi> <m:msubsup> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mo>˙</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent=true> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant=double-struck>R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> H{dot{K}}_{overrightarrow{q},overrightarrow{a}}^{alpha ,p}left({{mathbb{R}}}^{n}) and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>H</m:mi> <m:msubsup> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent=true> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant=double-struck>R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> H{K}_{overrightarrow{q},overrightarrow{a}}^{alpha ,p}left({{mathbb{R}}}^{n}) , on which atomic decomposition and molecular decomposition are obtained. Moreover, we gain the boundedness of classical Calderón-Zygmund operators." @default.
• W4386389681 created "2023-09-03" @default.
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• W4386389681 title "Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications" @default.
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