Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces | Zendy

Tomasz Adamowicz | Zendy; Petteri Harjulehto | Zendy; Peter Hästö | Zendy

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Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces

Author(s) -

Tomasz Adamowicz,

Petteri Harjulehto,

Peter Hästö

Publication year - 2015

Publication title -

mathematica scandinavica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.553

H-Index - 30

eISSN - 1903-1807

pISSN - 0025-5521

DOI - 10.7146/math.scand.a-20448

Subject(s) - mathematics , measure (data warehouse) , standard probability space , lp space , maximal operator , radon measure , operator (biology) , lebesgue measure , exponent , metric space , space (punctuation) , metric (unit) , pure mathematics , mathematical analysis , discrete mathematics , combinatorics , lebesgue integration , banach space , locally compact space , bounded function , biochemistry , chemistry , linguistics , philosophy , operations management , repressor , database , computer science , transcription factor , economics , gene

We study the Hardy-Littlewood maximal operator $M$ on $L^{p({\cdot})}(X)$ when $X$ is an unbounded (quasi)metric measure space, and $p$ may be unbounded. We consider both the doubling and general measure case, and use two versions of the $\log$-Holder condition. As a special case we obtain the criterion for a boundedness of $M$ on $L^{p({\cdot})}({\mathsf{R}^n},\mu)$ for arbitrary, possibly non-doubling, Radon measures.

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