Endpoint bounds for convolution operators with singular measures

@article{Ferreyra1998,
abstract = {Let $S\subset \mathbb \{R\}^\{n+1\}$ be the graph of the function $\varphi :[ -1,1]^n\rightarrow \mathbb \{R\}$ defined by $\varphi ( x_1,\dots ,x_n) =\sum _\{j=1\}^n| x_j|^\{\beta _j\},$ with 1<$\beta _1\le \dots \le \beta _n,$ and let $\mu $ the measure on $\mathbb \{R\}^\{n+1\}$ induced by the Euclidean area measure on S. In this paper we characterize the set of pairs (p,q) such that the convolution operator with $\mu $ is $L^p$-$L^q$ bounded.},
author = {Ferreyra, E., Godoy, T., Urciuolo, M.},
journal = {Colloquium Mathematicae},
keywords = {convolution; singular measure},
language = {eng},
number = {1},
pages = {35-47},
title = {Endpoint bounds for convolution operators with singular measures},
url = {http://eudml.org/doc/210551},
volume = {76},
year = {1998},
}

TY - JOUR
AU - Ferreyra, E.
AU - Godoy, T.
AU - Urciuolo, M.
TI - Endpoint bounds for convolution operators with singular measures
JO - Colloquium Mathematicae
PY - 1998
VL - 76
IS - 1
SP - 35
EP - 47
AB - Let $S\subset \mathbb {R}^{n+1}$ be the graph of the function $\varphi :[ -1,1]^n\rightarrow \mathbb {R}$ defined by $\varphi ( x_1,\dots ,x_n) =\sum _{j=1}^n| x_j|^{\beta _j},$ with 1<$\beta _1\le \dots \le \beta _n,$ and let $\mu $ the measure on $\mathbb {R}^{n+1}$ induced by the Euclidean area measure on S. In this paper we characterize the set of pairs (p,q) such that the convolution operator with $\mu $ is $L^p$-$L^q$ bounded.
LA - eng
KW - convolution; singular measure
UR - http://eudml.org/doc/210551
ER -