Zobrazeno 1 - 10
of 148
pro vyhledávání: '"Stein, Elias M."'
We prove convergence in norm and pointwise almost everywhere on $L^p$, $p\in (1,\infty)$, for certain multi-parameter polynomial ergodic averages by establishing the corresponding multi-parameter maximal and oscillation inequalities. Our result, in p
Externí odkaz:
http://arxiv.org/abs/2209.07358
Autor:
Lanzani, Loredana, Stein, Elias M.
We survey recent work and announce new results concerning two singular integral operators whose kernels are holomorphic functions of the output variable, specifically the Cauchy-Leray integral and the Cauchy-Szeg\H o projection associated to various
Externí odkaz:
http://arxiv.org/abs/1901.03402
This is a survey article about recent developments in dimension-free estimates for maximal functions corresponding to the Hardy--Littlewood averaging operators associated with convex symmetric bodies in $\mathbb R^d$ and $\mathbb Z^d$.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/1812.00153
Publikováno v:
Adv. Math. 365 (2020)
We prove strong jump inequalities for a large class of operators of Radon type in the discrete and ergodic theoretical settings. These inequalities are the $r=2$ endpoints of the $r$-variational estimates studied in arXiv:1512.07523.
Comment: v2
Comment: v2
Externí odkaz:
http://arxiv.org/abs/1809.03803
Publikováno v:
Analysis & PDE 13 (2020) 527-558
The aim of this paper is to present an abstract and general approach to jump inequalities in harmonic analysis. Our principal conclusion is the refinement of $r$-variational estimates, previously known for $r>2$, to end-point results for the jump qua
Externí odkaz:
http://arxiv.org/abs/1808.09048
Publikováno v:
Math. Ann. 376.1-2 (2020), pp. 797-819
Jump inequalities are the $r=2$ endpoint of L\'epingle's inequality for $r$-variation of martingales. Extending earlier work by Pisier and Xu we interpret these inequalities in terms of Banach spaces which are real interpolation spaces. This interpre
Externí odkaz:
http://arxiv.org/abs/1808.04592
Dimension-free bounds will be provided in maximal and $r$-variational inequalities on $\ell^p(\mathbb Z^d)$ corresponding to the discrete Hardy-Littlewood averaging operators defined over the cubes in $\mathbb Z^d$. We will also construct an example
Externí odkaz:
http://arxiv.org/abs/1804.07679
We study dimension-free $L^p$ inequalities for $r$-variations of the Hardy--Littlewood averaging operators defined over symmetric convex bodies in $\mathbb R^d$.
Comment: 27 pages, added applications to ergodic theory, to appear in GAFA
Comment: 27 pages, added applications to ergodic theory, to appear in GAFA
Externí odkaz:
http://arxiv.org/abs/1708.04639
Autor:
Lanzani, Loredana, Stein, Elias M.
The purpose of this paper is to complement the results in [LS-1] by showing the dense definability of the Cauchy-Leray transform for the domains that give the counterexamples of [LS-1], where $L^p$-boundedness is shown to fail when either the "near"
Externí odkaz:
http://arxiv.org/abs/1704.05381