L p -improving properties of measures supported on curves on the Heisenberg group. II

Silvia Secco

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 2, page 527-543
  • ISSN: 0392-4041

Abstract

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L p - L q estimates are obtained for convolution operators by finite measures supported on curves in the Heisenberg group whose tangent vector at the origin is parallel to the centre of the group.

How to cite

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Secco, Silvia. "$L^p$-improving properties of measures supported on curves on the Heisenberg group. II." Bollettino dell'Unione Matematica Italiana 5-B.2 (2002): 527-543. <http://eudml.org/doc/195307>.

@article{Secco2002,
abstract = {$L^\{p\}$-$L^\{q\}$ estimates are obtained for convolution operators by finite measures supported on curves in the Heisenberg group whose tangent vector at the origin is parallel to the centre of the group.},
author = {Secco, Silvia},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {convolution operator; characteristic set},
language = {eng},
month = {6},
number = {2},
pages = {527-543},
publisher = {Unione Matematica Italiana},
title = {$L^p$-improving properties of measures supported on curves on the Heisenberg group. II},
url = {http://eudml.org/doc/195307},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Secco, Silvia
TI - $L^p$-improving properties of measures supported on curves on the Heisenberg group. II
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/6//
PB - Unione Matematica Italiana
VL - 5-B
IS - 2
SP - 527
EP - 543
AB - $L^{p}$-$L^{q}$ estimates are obtained for convolution operators by finite measures supported on curves in the Heisenberg group whose tangent vector at the origin is parallel to the centre of the group.
LA - eng
KW - convolution operator; characteristic set
UR - http://eudml.org/doc/195307
ER -

References

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  1. HÖRMANDER, L., Estimates for translation invariant operators in L p spaces, Acta Math., 104 (1960), 93-139. Zbl0093.11402MR121655
  2. OBERLIN, D., Convolution estimates for some measures on curves, Proc. Amer. Math. Soc., 99 (1987), 56-60. Zbl0613.43002MR866429
  3. PAN, Y., A remark on convolution with measures supported on curves, Canad. Math. Bull., 36 (1993), 245-250. Zbl0820.43002MR1222541
  4. RICCI, F., Limitatezza L p - L q per operatori di convoluzione definiti da misure singolari in R n , Boll. Un. Mat. Ital., A 11 (1997), 237-252. Zbl0946.42006
  5. RICCI, F.- STEIN, E. M., Harmonic analysis on nilpotent groups and singular integrals. III. Fractional integration along manifolds, J. Funct. Anal., 86 (1989), 360-389. Zbl0684.22006MR1021141
  6. SECCO, S., Fractional integration along homogeneous curves in R 3 , Math. Scand., 85 (1999), 259-270. Zbl0971.42010MR1724238
  7. SECCO, S., L p -improving properties of measures supported on curves on the Heisenberg group, Studia Math., 132 (2) (1999), 179-201. Zbl0960.43009MR1669682

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