TY - JOUR
T1 - A boundedness criterion for the maximal operator on variable Lebesgue spaces
AU - Lerner, Andrei K.
N1 - Publisher Copyright:
© The Author(s) 2025.
PY - 2025
Y1 - 2025
N2 - We obtain a necessary and sufficient condition on an exponent p(·) for which the Hardy–Littlewood maximal operator is bounded on the variable Lp(·) space. It is formulated in terms of the Muckenhoupt-type condition Ap(·), 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.
AB - We obtain a necessary and sufficient condition on an exponent p(·) for which the Hardy–Littlewood maximal operator is bounded on the variable Lp(·) space. It is formulated in terms of the Muckenhoupt-type condition Ap(·), 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.
UR - https://www.scopus.com/pages/publications/105010769542
U2 - 10.1007/s11854-025-0383-2
DO - 10.1007/s11854-025-0383-2
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AN - SCOPUS:105010769542
SN - 0021-7670
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
ER -