Endpoint bounds for convolution operators with singular measures

Ferreyra, E.; Godoy, T.; Urciuolo, M.

Colloquium Mathematicae, Tome 78 (1998), p. 35-47 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $S \subset ℝ^{n + 1}$ be the graph of the function $ϕ : {[- 1, 1]}^{n} \to ℝ$ defined by $ϕ (x_{1}, \dots, x_{n}) = \sum_{j = 1}^{n} {| x_{j} |}^{β_{j}},$ with 1< $β_{1} \leq \dots \leq β_{n},$ and let $μ$ 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 $μ$ is $L^{p}$ - $L^{q}$ bounded.

Publié le : 1998-01-01

Zbl 0915.42009

EUDML-ID : urn:eudml:doc:210551

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     author = {E. Ferreyra and T. Godoy and M. Urciuolo},
     title = {Endpoint bounds for convolution operators with singular measures},
     journal = {Colloquium Mathematicae},
     volume = {78},
     year = {1998},
     pages = {35-47},
     zbl = {0915.42009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv76z1p35bwm}
}

Ferreyra, E.; Godoy, T.; Urciuolo, M. Endpoint bounds for convolution operators with singular measures. Colloquium Mathematicae, Tome 78 (1998) pp. 35-47. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv76z1p35bwm/

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