The weighted discrete Gehring classes, Muckenhoupt classes and their basic properties,Proceedings of the American Mathematical Society

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The weighted discrete Gehring classes, Muckenhoupt classes and their basic properties
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-10-09 , DOI: 10.1090/proc/15180
Samir Saker , Mario Krnić

Abstract:The main objective of this paper is a study of the structure and basic properties of the weighted discrete Gehring classes, as well as the study of the relationship between discrete Muckenhoupt and Gehring classes. First, we prove that the weighted discrete Muckenhoupt class $\mathcal {A}_{\lambda }^{1}(C)$ ,

, consisting of nonincreasing sequences, belongs to the weighted discrete Gehring class $\mathcal {G}_{\lambda }^{p}(A)$ by giving explicit values of exponent

and constant

. Next, we prove the self-improving property of the weighted Gehring class $\mathcal {G}_{\lambda }^{p}({K)}$ ,

, consisting of nonincreasing sequences. The exponent and constant of transition are explicitly given. Finally, utilizing the self-improving property of the weighted Gehring class, we also derive the self-improving property of a discrete Muckenhoupt class $\mathcal {A}^{p}(C)$ ,

, with exact values of exponent and constant of transition.

中文翻译：

加权离散Gehring类，Mukenhoupt类及其基本属性

摘要：本文的主要目的是研究加权离散Gehring类的结构和基本性质，以及研究离散Muckenhoupt与Gehring类之间的关系。首先，我们证明了加权离散Muckenhoupt类，，由非增序列的，属于加权离散Gehring集团类通过给出指数的显式值和常数。接下来，我们证明了加权Gehring集团类的自我改进的性能，， $\ mathcal {A} _ {\ lambda} ^ {1}（C）$

$\ mathcal {G} _ {\ lambda} ^ {p}（A）$

$\ mathcal {G} _ {\ lambda} ^ {p}（{K）}$

，由非递增序列组成。明确给出了过渡的指数和常数。最后，利用加权Gehring集团类的自我改进的性能，我们还得到一个离散Muckenhoupt类的自我改进的性能，，，与指数和过渡的常数的精确值。 $\ mathcal {A} ^ {p}（C）$

更新日期：2020-11-12

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