This book discusses advances in maximal function methods related to Poincaré and
Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's …

We study the regularity properties of the centered fractional maximal function M β. More
precisely, we prove that the map f↦|∇ M β f| is bounded and continuous from W 1, 1 (R d) to …

The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing
estimates and their applications. After reviewing the classical background, we describe …

We establish continuity mapping properties of the noncentered fractional maximal operator
in the endpoint input space for in the cases for which its boundedness is known. More …

BV continuity for the uncentered Hardy–Littlewood maximal operator - ScienceDirect Skip to
main contentSkip to article Elsevier logo Journals & Books Search RegisterSign in View PDF …

This is an expository paper on the regularity theory of maximal operators, when these act on
Sobolev and BV functions, with a special focus on some of the current open problems in the …

In this paper we study the regularity properties of certain maximal operators of convolution
type at the endpoint $ p= 1$, when acting on radial data. In particular, for the heat flow …

In this paper, our object of investigation is the endpoint regularity of the following general
maximal operator, M~ Φ f (x)= sup r, s≥ 0 r+ s> 0 Φ (r+ s)∫ x-rx+ s| f (y)| dy, and minimal …

We establish that the map $ f\mapsto|\nabla\mathcal {M} _ {\alpha} f| $ is continuous from $
W^{1, 1}(\mathbb {R}^ d) $ to $ L^{q}(\mathbb {R}^ d) $, where $\alpha\in (0, d) $, $ q=\frac …

We consider the maximal operator with respect to uncentered cubes on Euclidean space
with arbitrary dimension. We prove that for any function with bounded variation, the variation …