A new <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>–<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msub></mml:math> estimate for Calderón–Zygmund operators in spaces of homogeneous type

Li, Kangwei

doi:10.1016/j.jmaa.2015.03.076

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2016

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“…We conclude the introduction by noting that our results already turned out to be useful in a recent paper by K. Li [20].…”

Section: Introductionmentioning

confidence: 59%

Weak $$A_\infty $$ Weights and Weak Reverse Hölder Property in a Space of Homogeneous Type

2016

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Abstract. In the Euclidean setting, the Fujii-Wilson-type A∞ weights satisfy a Reverse Hölder Inequality (RHI) but in spaces of homogeneous type the best known result has been that A∞ weights satisfy only a weak Reverse Hölder Inequality. In this paper, we compliment the results of Hytönen, Pérez and Rela and show that there exist both A∞ weights that do not satisfy an RHI and a genuinely weaker weight class that still satisfies a weak RHI. We also show that all the weights that satisfy a weak RHI have a self-improving property but the self-improving property of the strong Reverse Hölder weights fails in a general space of homogeneous type. We prove most of these purely non-dyadic results using convenient dyadic systems and techniques.

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“…We conclude the introduction by noting that our results already turned out to be useful in a recent paper by K. Li [20].…”

Section: Introductionmentioning

confidence: 59%

Weak $$A_\infty $$ Weights and Weak Reverse Hölder Property in a Space of Homogeneous Type

2016

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A new Ap–A∞ estimate for Calderón–Zygmund operators in spaces of homogeneous type

Abstract: In this note, we study the A p -A ∞ estimate for Calderón-Zygmund operators in terms of the weak A ∞ characteristics in spaces of homogeneous type. The weak A ∞ class was introduced recently by Anderson, Hytönen and Tapiola. Our estimate is new even in Euclidean space.

Cited by 1 publication

References 18 publications

Weak $$A_\infty $$ Weights and Weak Reverse Hölder Property in a Space of Homogeneous Type

Weak $$A_\infty $$ Weights and Weak Reverse Hölder Property in a Space of Homogeneous Type

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