Local sharp maximal functions

Weighted Rearrangement Inequalities for Local Sharp Maximal Functions

Several weighted rearrangement inequalities for uncentered and centered local sharp functions are proved. These results are applied to obtain new weighted weak-type and strong-type estimates for singular integrals. A self-improving property of sharp function inequalities is established.

Weighted Norm Inequalities for the Local Sharp Maximal Function

Sharp Inequalities for Maximal Functions Associated with General Measures

Sharp weak type (1, 1) and L p estimates in dimension one are obtained for uncentered maximal functions associated with Borel measures which do not necessarily satisfy a doubling condition. In higher dimensions uncentered maximal functions fail to satisfy such estimates. Analogous results for centered maximal functions are given in all dimensions.

Rearrangements and the Local Integrablility of Maximal Functions

Let MHL and MS respectively denote the Hardy–Littlewood and strong maximal operators, and let Mx and My respectively denote the one-dimensional Hardy–Littlewood maximal operators in the horizontal and vertical directions in R. It is well known that if f and f̃ are equidistributed functions supported on Q = [0, 1] × [0, 1], then ∫ Q MHLf ∼ ∫ Q MHLf̃ . This article examines the relationships betwee...

On Some Pointwise Inequalities concerning Tent Spaces and Sharp Maximal Functions

We consider an abstract analogue of S λ f , the truncated square function introduced by J.-O. Strömberg, and show that it is closely related to operators appearing in the theory of tent spaces. We suggest an approach to basic results for these spaces which differs from that due to R.R. Coifman, Y. Meyer and E.M. Stein. Also we discuss pointwise estimates involving S λ f as well as different var...