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- W3213233722 abstract "Abstract We study the higher integrability of weights satisfying a reverse Hölder inequality <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msup> <m:mrow> <m:mo maxsize=210% minsize=210%>(</m:mo> <m:mrow> <m:msub> <m:mo largeop=true symmetric=true>⨏</m:mo> <m:mi>I</m:mi> </m:msub> <m:msup> <m:mi>u</m:mi> <m:mi>β</m:mi> </m:msup> </m:mrow> <m:mo maxsize=210% minsize=210%>)</m:mo> </m:mrow> <m:mfrac> <m:mn>1</m:mn> <m:mi>β</m:mi> </m:mfrac> </m:msup> <m:mo>≤</m:mo> <m:mrow> <m:mi>B</m:mi> <m:mo></m:mo> <m:msup> <m:mrow> <m:mo maxsize=210% minsize=210%>(</m:mo> <m:mrow> <m:msub> <m:mo largeop=true symmetric=true>⨏</m:mo> <m:mi>I</m:mi> </m:msub> <m:msup> <m:mi>u</m:mi> <m:mi>α</m:mi> </m:msup> </m:mrow> <m:mo maxsize=210% minsize=210%>)</m:mo> </m:mrow> <m:mfrac> <m:mn>1</m:mn> <m:mi>α</m:mi> </m:mfrac> </m:msup> </m:mrow> </m:mrow> </m:math> {biggl{(}fint_{I}u^{beta}biggr{)}^{frac{1}{beta}}}leq B{biggl{(}fint_{I}u^{alpha}biggr{)}^{frac{1}{alpha}}} for some <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>B</m:mi> <m:mo>></m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> B>1 and given <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>α</m:mi> <m:mo><</m:mo> <m:mi>β</m:mi> </m:mrow> </m:math> alpha<beta , in the limit cases when <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>α</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo stretchy=false>{</m:mo> <m:mrow> <m:mo>-</m:mo> <m:mi mathvariant=normal>∞</m:mi> </m:mrow> <m:mo>,</m:mo> <m:mn>0</m:mn> <m:mo stretchy=false>}</m:mo> </m:mrow> </m:mrow> </m:math> alphain{-infty,0} and/or <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>β</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo stretchy=false>{</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mrow> <m:mo>+</m:mo> <m:mi mathvariant=normal>∞</m:mi> </m:mrow> <m:mo stretchy=false>}</m:mo> </m:mrow> </m:mrow> </m:math> betain{0,+infty} . The results apply to the Gehring and Muckenhoupt weights and their corresponding limit classes." @default.
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- W3213233722 date "2021-11-10" @default.
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- W3213233722 title "Higher integrability and reverse Hölder inequalities in the limit cases" @default.
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- W3213233722 doi "https://doi.org/10.1515/gmj-2021-2116" @default.
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