We consider maximal operators MBMB with respect to a basis BB. In the case when MBMB satisfies a reversed weak type inequality, we obtain a boundedness criterion for MBMB on an arbitrary quasi-Banach function space XX. ...

In this paper a space X is pseudocompact if it is Tychonoff and every real-valued continuous function on X is bounded. We obtain conditions under which a Tychonoff space is maximal pseudocompact and study conditions under ...

In this work we characterize the pairs of weights (w, v) such that the one-sided Hardy-Littlewood maximal function in dimension two is of weak-type (p, p), 1 ≤ p ≤ ∞, with respect to the pair (w, v). As an application of ...

Given a rotation invariant measure in Rn, we define the maximal operator over circular sectors. We prove that it is of strong type (p,p) for p>1 and we give necessary and sufficient conditions on the measure for the weak ...

The purpose of this paper is to prove the Lp(Rn, dγ) boundedness, for p > 1, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure dγ = e-|x|(2) dx.

We consider the maximal operator defined on the real line by which is related to the Cesàro convergence of the singular integrals. We characterize the weights w for which Mα is of weak type, strong type and restricted weak ...

In this paper we establish that the set of Lipschitz functions f : U → R (U a nonempty open subset of ` 1 d ) with maximal Clarke subdifferential contains a linear subspace of uncountable dimension (in particular, an ...

In this work we obtain boundedness on BMO and Lipschitz type spaces in the context of a critical radius function. We deal with a local maximal operator and a maximal operator of a one parameter family of operators with ...

We obtain a comparison of the level sets for two maximal functions on a space of homogeneous type: the Hardy-Littlewood maximal function of mean values over balls and the dyadic maximal function of mean values over the ...

Representation formulas for faces and support functions of the values of maximal monotone operators are established in two cases: either the operators are defined on reflexive and locally uniformly convex real Banach spaces ...