Endpoint bounds for convolution operators with singular measures
Colloquium Mathematicum, Tome 76 (1998) no. 1, pp. 35-47
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Let $S\subset \R^{n+1}$ be the graph of the function $\varphi:[ -1,1]^n\rightarrow \R $ defined by $\varphi ( x_1,\dots,x_n) =\sum_{j=1}^n| x_j|^{\beta_j},$ with 1$\beta_1\leq \dots \leq \beta_n,$ and let $\mu $ the measure on $\R^{n+1}$ 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.
@article{10_4064_cm_76_1_35_47,
author = {E. Ferreyra and T. Godoy and M. Urciuolo},
title = {Endpoint bounds for convolution operators with singular measures},
journal = {Colloquium Mathematicum},
pages = {35--47},
publisher = {mathdoc},
volume = {76},
number = {1},
year = {1998},
doi = {10.4064/cm-76-1-35-47},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-76-1-35-47/}
}
TY - JOUR AU - E. Ferreyra AU - T. Godoy AU - M. Urciuolo TI - Endpoint bounds for convolution operators with singular measures JO - Colloquium Mathematicum PY - 1998 SP - 35 EP - 47 VL - 76 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm-76-1-35-47/ DO - 10.4064/cm-76-1-35-47 LA - en ID - 10_4064_cm_76_1_35_47 ER -
%0 Journal Article %A E. Ferreyra %A T. Godoy %A M. Urciuolo %T Endpoint bounds for convolution operators with singular measures %J Colloquium Mathematicum %D 1998 %P 35-47 %V 76 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm-76-1-35-47/ %R 10.4064/cm-76-1-35-47 %G en %F 10_4064_cm_76_1_35_47
E. Ferreyra; T. Godoy; M. Urciuolo. Endpoint bounds for convolution operators with singular measures. Colloquium Mathematicum, Tome 76 (1998) no. 1, pp. 35-47. doi: 10.4064/cm-76-1-35-47
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