Endpoint bounds for convolution operators with singular measures

Volume 76 / 1998

E. Ferreyra, T. Godoy, M. Urciuolo Colloquium Mathematicum 76 (1998), 35-47 DOI: 10.4064/cm-76-1-35-47


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.


  • E. Ferreyra
  • T. Godoy
  • M. Urciuolo

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