Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type

Xi Cen

doi:10.1007/s13324-024-00955-6

Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type

Classical Analysis and ODEs 2024-08-13 v3 Functional Analysis

Authors: Xi Cen

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Abstract

Let $(X,d,\mu)$ is a space of homogeneous type, we establish a new class of fractional-type variable weights $A_{p(\cdot), q(\cdot)}(X)$ . Then, we get the new weighted strong-type and weak-type characterizations for fractional maximal operators $M_\eta$ on weighted variable Lebesgue spaces over $(X,d,\mu)$ . This study generalizes the results by Cruz-Uribe-Fiorenza-Neugebauer (2012), Bernardis-Dalmasso-Pradolini (2014), Cruz-Uribe-Shukla (2018), and Cruz-Uribe-Cummings (2022).

Keywords

fractional maximal operators weighted variable Lebesgue spaces spaces of homogeneous type fractional-type variable weights strong-type weak-type characterizations

Cite

@article{arxiv.2404.15550,
  title  = {Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type},
  author = {Xi Cen},
  journal= {arXiv preprint arXiv:2404.15550},
  year   = {2024}
}

Comments

In the officially published documents, there is a symbol error in Theorem 1.10 and there is an additional reference in the References. We have corrected these mistakes

Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type

Abstract

Keywords

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