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

Studia Mathematica (1999)

- Volume: 132, Issue: 2, page 179-201
- ISSN: 0039-3223

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topSecco, Silvia. "$L^p$-improving properties of measures supported on curves on the Heisenberg group." Studia Mathematica 132.2 (1999): 179-201. <http://eudml.org/doc/216594>.

@article{Secco1999,

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.},

author = {Secco, Silvia},

journal = {Studia Mathematica},

keywords = {Heisenberg group; measure; convolution operator; boundedness properties},

language = {eng},

number = {2},

pages = {179-201},

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

url = {http://eudml.org/doc/216594},

volume = {132},

year = {1999},

}

TY - JOUR

AU - Secco, Silvia

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

JO - Studia Mathematica

PY - 1999

VL - 132

IS - 2

SP - 179

EP - 201

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

LA - eng

KW - Heisenberg group; measure; convolution operator; boundedness properties

UR - http://eudml.org/doc/216594

ER -

## References

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- [3] D. Oberlin, Convolution estimates for some measures on curves, Proc. Amer. Math. Soc. 99 (1987), 56-60. Zbl0613.43002
- [4] Y. Pan, A remark on convolution with measures supported on curves, Canad. Math. Bull. 36 (1993), 245-250. Zbl0820.43002
- [5] Y. Pan, Convolution estimates for some degenerate curves, Math. Proc. Cambridge Philos. Soc. 116 (1994), 143-146. Zbl0812.42006
- [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. Zbl0684.22006
- [8] S. Secco, Fractional integration along homogeneous curves in ${\mathbb{R}}^{3}$, preprint.

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