# Endpoint bounds for convolution operators with singular measures

E. Ferreyra; T. Godoy; M. Urciuolo

Colloquium Mathematicae (1998)

- Volume: 76, Issue: 1, page 35-47
- ISSN: 0010-1354

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topFerreyra, E., Godoy, T., and Urciuolo, M.. "Endpoint bounds for convolution operators with singular measures." Colloquium Mathematicae 76.1 (1998): 35-47. <http://eudml.org/doc/210551>.

@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 -

## References

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- [F-G-U] Ferreyra E., Godoy T. and Urciuolo M., ${L}^{p}$-${L}^{q}$ estimates for convolution operators with $n$-dimensional singular measures, J. Fourier Anal. Appl., to appear.
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- [St] Stein E.M. , Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993.
- [S-W] Stein E. and Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.

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