On Sufficient Conditions for the Boundedness of the Hardy-Littlewood Maximal Operator between Weighted Lp -Spaces with Different Weights

On the Lp boundedness of the non-centered Gaussian Hardy-Littlewood Maximal Function

The purpose of this paper is to prove the L p (R n ; dd) boundedness, for p > 1, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure dd = e ?jxj 2 dx. Let dd = e ?jxj 2 dx be a Gaussian measure in Euclidean space R n. We consider the non-centered maximal function deened by Mf(x) = sup x2B 1 (B) Z B jfj dd; where the supremum is taken over all balls B in R ...

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...

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...

ACTA UNIVERSITATIS APULENSIS No 19/2009 BOUNDEDNESS FOR MULTILINEAR COMMUTATOR OF LITTLEWOOD-PALEY OPERATOR ON HARDY AND HERZ-HARDY SPACES

In this paper, the (H ~b , L p) and (HK̇ q,~b , K̇ q ) type boundedness for the multilinear commutator associated with the Littlewood-paley operator are obtained.

On Boundedness of Weighted Hardy Operator in Lp() and Regularity Condition