On some questions related to the maximal operator on variable $L^p$ spaces
نویسندگان
چکیده
منابع مشابه
On Some Questions Related to the Maximal Operator on Variable L Spaces
Let P(Rn) be the class of all exponents p for which the HardyLittlewood maximal operator M is bounded on Lp(·)(Rn). A recent result by T. Kopaliani provides a characterization of P in terms of the Muckenhoupttype condition A under some restrictions on the behavior of p at infinity. We give a different proof of a slightly extended version of this result. Then we characterize a weak type ( p(·), ...
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where the supremum is taken over all cubes Q ⊂ R containing the point x. In [5], L. Diening proved the following remarkable result: if p− > 1, p+ < ∞ and M is bounded on Lp(·), then M is bounded on L (·), where p′(x) = p(x) p(x)−1 . Despite its apparent simplicity, the proof in [5] is rather long and involved. In this paper we extend Diening’s theorem to weighted variable Lebesgue spaces L p(·)...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2010
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-10-05066-x