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For a given set of dilations $E\subset [1,2]$, Lebesgue space mapping properties of the spherical maximal operator with dilations restricted to $E$ are studied when acting on radial functions. In higher dimensions, the type set only depends on the up
Externí odkaz:
http://arxiv.org/abs/2412.09390
Autor:
Wheeler, Reuben
We study $L^p\rightarrow L^q(V^r_E)$ variation semi-norm estimates for the spherical averaging operator, where $E\subset [1,2]$.
Comment: 25 pages, 3 figures
Comment: 25 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/2409.05579
Autor:
Roos, Joris, Seeger, Andreas
Publikováno v:
Amer. J. Math. 145 (2023), no. 4, 1077--1110
For the spherical mean operators $\mathcal{A}_t$ in $\mathbb{R}^d$, $d\ge 2$, we consider the maximal functions $M_Ef =\sup_{t\in E} |\mathcal{A}_t f|$, with dilation sets $E\subset [1,2]$. In this paper we give a surprising characterization of the c
Externí odkaz:
http://arxiv.org/abs/2004.00984
Publikováno v:
Mathematische Zeitschrift, 297 (2021), 1057-1074
Let $f\in L^p(\mathbb{R}^d)$, $d\ge 3$, and let $A_t f(x)$ the average of $f$ over the sphere with radius $t$ centered at $x$. For a subset $E$ of $[1,2]$ we prove close to sharp $L^p\to L^q$ estimates for the maximal function $\sup_{t\in E} |A_t f|$
Externí odkaz:
http://arxiv.org/abs/1909.05389
Autor:
Laba, Izabella
For $2\leq p<\infty$, $\alpha'>2/p$, and $\delta>0$, we construct Cantor-type measures on $\mathbb{R}$ supported on sets of Hausdorff dimension $\alpha<\alpha'$ for which the associated maximal operator is bounded from $L^p_\delta (\mathbb{R})$ to $L
Externí odkaz:
http://arxiv.org/abs/1808.05657