Results 1 to 10 of about 1,166,647 (124)
The elliptic maximal function [PDF]
arXiv, 2023 We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq \infty$. For this purpose, we obtain some sharp multi-parameter local smoothing estimates.
arxiv
Nikodym sets and maximal functions associated with spheres [PDF]
arXiv, 2022 We study spherical analogues of Nikodym sets and related maximal functions. In particular, we prove sharp $L^p$-estimates for Nikodym maximal functions associated with spheres. As a corollary, any Nikodym set for spheres must have full Hausdorff dimension.
arxiv
On the regularity of the maximal function of a BV function [PDF]
arXiv, 2020 We show that the non-centered maximal function of a BV function is quasicontinuous. We also show that \emph{if} the non-centered maximal functions of an SBV function is a BV function, then it is in fact a Sobolev function. Using a recent result of Weigt, we are in particular able to show that the non-centered maximal function of a set of finite ...
arxiv
Two-weight inequalities for multilinear maximal functions in Orlicz spaces [PDF]
arXiv, 2022 In this note, we provide various two-weight norm estimates of the multi-linear fractional maximal function and weighted maximal function between different Orlicz spaces. More precisely, we obtain Sawyer-type characterizations and norm estimates for these operators.
arxiv
A note on maximal plurifinely plurisubharmonic functions [PDF]
arXiv, 2017 In this note we study the plurifinely locally maximal plurifinely plurisubharmonic functions and improve some known results on these functions. We prove in particular that any locally bounded plurifinely locally maximal plurifinely plurisubharmonic function is maximal, and that any finite plurisubharmonic function on an open subset of $\mathbb{C}^n$ is
arxiv
Maximal subextension and stability on $m$-capacity of maximal subextension of $m$-subharmonic functions with given boundary values [PDF]
arXiv, 2023 In this paper, we study maximal subextension of $m$-subharmonic functions with given boundary values. We also prove stability on $m$-capacity of maximal subextension of $m$-subharmonic functions with given boundary values.
arxiv
Maximal operators on BMO and slices [PDF]
arXiv, 2023 We prove that the Hardy-Littlewood maximal operator is discontinuous on $\bmorn$ and maps $\vmorn$ to itself. A counterexample to boundedness of the strong and directional maximal operators on $\bmorn$ is given, and properties of slices of $\bmorn$ functions are discussed.
arxiv
A note on the Gaussian maximal functions [PDF]
arXiv, 2013 This note presents a proof that the non-tangential maximal function of the Ornstein-Uhlenbeck semigroup is bounded almost surely by the Gaussian Hardy-Littlewood maximal function. In particular this entails improvement on a result by Pineda and Urbina who proved a similar result for a `trunctated' version of the non-tangential maximal function.
arxiv
Sobolev spaces, Lebesgue points and maximal functions [PDF]
arXiv, 2013 In this note we study boundedness of a large class of maximal operators in Sobolev spaces that includes the spherical maximal operator. We also study the size of the set of Lebesgue points with respect to convergence associated with such maximal operators.
arxiv
Maximal functions and measures on the upper-half plane [PDF]
arXiv, 2017 We study weighted boundedness of Hardy-Littlewood-type maximal function involving Orlicz functions. We also obtain some sufficient conditions for the weighted boundedness of the Hardy-Littlewood maximal function of the upper-half plane.
arxiv