Local Hardy--Littlewood maximal operator in variable Lebesgue spaces

Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

Weighted L for p ∈ 1,∞ and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. Al...

Orlicz Spaces for Which the Hardy-littlewood Maximal Operator Is Bounded

Mathematische Zeitschrift Some remarks on the Hardy-Littlewood maximal function on variable L spaces

We show that any pointwise multiplier for BMO(R) generates a function p from the class P(Rn) of those functions for which the Hardy-Littlewood maximal operator is bounded on the variable L space. In particular, this gives a positive answer to Diening’s conjecture saying that there are discontinuous functions which nevertheless belong to P(Rn). Mathematics Subject Classification (2000): 42B25

Boundedness for Multilinear Commutator of Littlewood-paley Operator on Hardy and Herz-hardy Spaces

Let 0 < q < ∞ and Lqloc(R n) = {f q is locally integrable on Rn}. Suppose f ∈ Lloc(R), B = B(x0, r) = {x ∈ Rn : |x − x0| < r} denotes a ball of Rn centered at x0 and having radius r, write fB = |B|−1 ∫ B f(x)dx and f #(x) = supx∈B |B|−1 ∫ B |f(x) − fB|dx < ∞. f is said to belong to BMO(R n), if f# ∈ L∞(Rn) and define ||f ||BMO = ||f||L∞ . Let T be the Calderón-Zygmund singular integral operator...

Affine Synthesis onto Lebesgue and Hardy Spaces

The affine synthesis operator Sc = P j>0 P k∈Zd cj,kψj,k is shown to map the mixed-norm sequence space `(`) surjectively onto L(R) under mild conditions on the synthesizer ψ ∈ L(R), 1 ≤ p < ∞, with R Rd ψ dx = 1. Here ψj,k(x) = |det aj |ψ(ajx−k), and the dilation matrices aj expand, for example aj = 2I . Affine synthesis further maps a discrete mixed Hardy space `(h) onto H(R). Therefore the H-...