On Boundedness of Maximal Operators Associated with Hypersurfaces

boundedness of maximal averages over hypersurfaces in R 3

Our goal is to determine for which p is the maximal operator M bounded on L. Note that by subadditivity of maximal operators of the form (1.1), one can prove L boundedness of the nonlocalized analogue of (1.1) over a compact surface by doing a partition of unity and reducing to (1.1). If L is an invertible linear transformation and ML denotes the maximal operator corresponding to the surface L(...

Boundedness of Maximal Operators and Maximal Commutators on Non-homogeneous Spaces

Let (X,μ) be a non-homogeneous space in the sense that X is a metric space equipped with an upper doubling measure μ. The aim of this paper is to study the endpoint estimate of the maximal operator associated to a Calderón-Zygmund operator T and the L boundedness of the maximal commutator with RBMO functions

Boundedness of Littlewood-Paley Operators Associated with Gauss Measures

Modeled on the Gauss measure, the authors introduce the locally doubling measure metric space X, d, μ ρ, which means that the set X is endowed with a metric d and a locally doubling regular Borel measure μ satisfying doubling and reverse doubling conditions on admissible balls defined via the metric d and certain admissible function ρ. The authors then construct an approximation of the identity...

ON THE BOUNDEDNESS OF MAXIMAL OPERATORS AND SINGULAR OPERATORS WITH KERNELS IN L(logL)alpha(Sn-1)

A Note on Maximal Operators Associated with Hankel Multipliers

Let m have compact support in (0,∞). For 1 < p < 2d/(d + 1), we give a necessary and sufficient condition for the Lprad(R )-boundedness of the maximal operator associated with the radial multiplier m(|ξ|). More generally we prove a similar result for maximal operators associated with multipliers of modified Hankel transforms. The result is obtained by modifying the proof of the characterization...