Note on local properties of the exponents and boundedness of Hardy-Littlewood maximal operator in variable Lebesgue spaces

Kopaliani, Tengiz; Zviadadze, Shalva

doi:10.14492/hokmj/1602036024

Hokkaido Math. J.

2020

DOI: 10.14492/hokmj/1602036024

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Note on local properties of the exponents and boundedness of Hardy-Littlewood maximal operator in variable Lebesgue spaces

Tengiz Kopaliani¹,

Shalva Zviadadze²

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2023

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“…Before we turn to our contribution, note that the exposition above is definitely not complete. In particular, let us also mention the works [3,4,10,12,15] dedicated to various aspects of the class P.…”

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confidence: 99%

A boundedness criterion for the maximal operator on variable Lebesgue spaces

Lerner¹

2023

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We obtain a necessary and sufficient condition on an exponent p(•) for which the Hardy-Littlewood maximal operator is bounded on the variable L p(•) space. It is formulated in terms of the Muckenhoupt-type condition A p(•) , responsible for a local control of p(•), and a certain integral condition on p(•), responsible for the behaviour of p(•) at infinity. Our approach is based on an earlier characterization established by L. Diening and on non-increasing rearrangements.2020 Mathematics Subject Classification. 42B25, 42B35.

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mentioning

confidence: 99%

A boundedness criterion for the maximal operator on variable Lebesgue spaces

Lerner¹

2023

Preprint

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Note on local properties of the exponents and boundedness of Hardy-Littlewood maximal operator in variable Lebesgue spaces

Cited by 1 publication

References 0 publications

A boundedness criterion for the maximal operator on variable Lebesgue spaces

A boundedness criterion for the maximal operator on variable Lebesgue spaces

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