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

• Autorzy: Silvia Secco
• Języki publikacji: EN

Abstrakty

EN

$L^p$-$L^q$ 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.

Kategorie tematyczne

• 43A80: Analysis on other specific Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 132
• Numer: 2
• Strony: 179-201

Daty

wydano

1999

otrzymano

1998-04-17

poprawiono

1998-05-18

Twórcy

autor

Silvia Secco

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

Bibliografia

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• [3] D. Oberlin, Convolution estimates for some measures on curves, Proc. Amer. Math. Soc. 99 (1987), 56-60.
• [4] Y. Pan, A remark on convolution with measures supported on curves, Canad. Math. Bull. 36 (1993), 245-250.
• [5] Y. Pan, Convolution estimates for some degenerate curves, Math. Proc. Cambridge Philos. Soc. 116 (1994), 143-146.
• [6] Y. Pan, $L^p$-improving properties for some measures supported on curves, preprint.
• [7] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. III. Fractional integration along manifolds, J. Funct. Anal. 86 (1989), 360-389.
• [8] S. Secco, Fractional integration along homogeneous curves in $ℝ^3$, preprint.