$L^p$-improving properties of measures supported on curves on the Heisenberg group

Silvia Secco

ArticleOriginal scientific text

Title

$L^{p}$ -improving properties of measures supported on curves on the Heisenberg group

Authors ¹

Affiliations

Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Abstract

L^{p}

-

L^{q}

boundedness properties are obtained for operators defined by convolution with measures supported on certain curves on the Heisenberg group. We find the curvature condition for which the type set of these operators can be the full optimal trapezoid with vertices A=(0,0), B=(1,1), C=(2/3,1/2), D=(1/2,1/3). We also give notions of right curvature and left curvature which are not mutually equivalent.

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Title

Lp-improving properties of measures supported on curves on the Heisenberg group

Affiliations

Abstract

Bibliography

$L^{p}$ -improving properties of measures supported on curves on the Heisenberg group