A different approach to boundedness of the B-maximal operators on the variable Lebesgue spaces
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi
Abstract
By using the
L
p
(
⋅
)
−
boundedness of a maximal operator defined on homogeneous space, it has been shown that the
B
−
maximal operator is bounded. In the present paper, we aim to bring a different approach to the boundedness of the
B
−
maximal operator generated by generalized translation operator under a continuity assumption on
p
(
⋅
)
. It is noteworthy to mention that our assumption is weaker than uniform Hölder continuity.
Description
Keywords
Maximal operator, singular integrals, variable Lebesgue space