Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

Intrinsic Square Functions on Morrey and Block Spaces with Variable Exponents

“…Notice that the Lebesgue spaces with variable exponents are members of the family of block spaces with variable exponents. Thus, the result in [7] for the Hardy-Littlewood maximal operators is a generalization of the boundedness of the Hardy-Littlewood maximal operator on L p(·) .…”

“…The classical block spaces are generalized to the block spaces with variable exponents in [7]. In [7], we also have the boundedness of the Hardy-Littlewood maximal operator on the block spaces with variable exponents.…”

“…In [7], we also have the boundedness of the Hardy-Littlewood maximal operator on the block spaces with variable exponents. Notice that the Lebesgue spaces with variable exponents are members of the family of block spaces with variable exponents.…”

“…They are pre-dual of the classical Morrey spaces. The block spaces with variable exponents were introduced in [7] and the boundedness of the Hardy-Littlewood maximal operator on block spaces with variable exponents was also obtained in [7]. We establish the boundedness of vector-valued intrinsic square function to block spaces with variable exponents in Sect.…”

Atomic decomposition of predictable martingale Hardy space with variable exponents

“…It should be mentioned that (L p(·) (R n ), · p(·) ) was introduced by Orlicz [20] in 1931 and studied by Kováčik and Rákos-ník [14], Fan and Zhao [8] and others. Heavily basing on the so-called log-Hölder continuity conditions in [6], namely, |p(x) − p(y)| c 1 log(e + 1/|x − y|) , x, y ∈ R n , harmonic analysis with variable exponents has got an increasing development in the past years; see [2]- [7], [10], [18], [19], [22] and so on. Especially, in [5], [18], [22], the atomic decompositions of Hardy spaces with variable exponents defined on R n were established under the so-called log-Hölder continuity conditions.…”