Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Tapiola, Olli"'
Suppose that $\Omega \subset\mathbb R^{n+1}$, $n\geq1$, is a uniform domain with $n$-Ahlfors regular boundary and $L$ is a (not necessarily symmetric) divergence form elliptic, real, bounded operator in $\Omega$. We show that the corresponding ellipt
Externí odkaz:
http://arxiv.org/abs/2302.13294
Autor:
Tapiola, Olli, Tolsa, Xavier
Publikováno v:
Analysis & PDE 17 (2024) 1831-1870
Inspired by recent work of Mourgoglou and the second named author, and earlier work of Hofmann, Mitrea and Taylor, we consider connections between the local John condition, the Harnack chain condition and weak boundary Poincar\'e inequalities in open
Externí odkaz:
http://arxiv.org/abs/2205.11667
Autor:
Hofmann, Steve, Tapiola, Olli
We construct extensions of Varopolous type for functions $f \in \text{BMO}(E)$, for any uniformly rectifiable set $E$ of codimension one. More precisely, let $\Omega \subset \mathbb{R}^{n+1}$ be an open set satisfying the corkscrew condition, with an
Externí odkaz:
http://arxiv.org/abs/2003.07749
We consider Coifman--Fefferman inequalities for rough homogeneous singular integrals $T_\Omega$ and $C_p$ weights. It was recently shown by Li-P\'erez-Rivera-R\'ios-Roncal that $$ \|T_\Omega \|_{L^p(w)} \le C_{p,T,w} \|Mf\|_{L^p(w)} $$ for every $0<
Externí odkaz:
http://arxiv.org/abs/1909.08344
Autor:
Bortz, Simon, Tapiola, Olli
Suppose that $\Omega \subset \mathbb{R}^{n+1}$, $n \ge 2$, is an open set satisfying the corkscrew condition with an $n$-dimensional ADR boundary, $\partial \Omega$. In this note, we show that if harmonic functions are $\varepsilon$-approximable in $
Externí odkaz:
http://arxiv.org/abs/1801.05996
Autor:
Hofmann, Steve, Tapiola, Olli
Suppose that $E \subset \mathbb{R}^{n+1}$ is a uniformly rectifiable set of codimension $1$. We show that every harmonic function is $\varepsilon$-approximable in $L^p(\Omega)$ for every $p \in (1,\infty)$, where $\Omega := \mathbb{R}^{n+1} \setminus
Externí odkaz:
http://arxiv.org/abs/1710.05528
We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound that is quadratic in the $A_2$
Externí odkaz:
http://arxiv.org/abs/1510.05789
Autor:
Tapiola, Olli
With the help of recent adjacent dyadic constructions by Hyt\"onen and the author, we give an alternative proof of results of Lechner, M\"uller and Passenbrunner about the $L^p$-boundedness of shift operators acting on functions $f \in L^p(X;E)$ wher
Externí odkaz:
http://arxiv.org/abs/1504.01596
In the Euclidean setting, the Fujii-Wilson-type $A_\infty$ weights satisfy a Reverse H\"older Inequality (RHI) but in spaces of homogeneous type the best known result has been that $A_\infty$ weights satisfy only a weak Reverse H\"older Inequality. I
Externí odkaz:
http://arxiv.org/abs/1410.3608