L p -estimates for singular integrals and maximal operators associated with flat curves on the Heisenberg group
Kim, Joonil
Duke Math. J., Tome 115 (2002) no. 1, p. 555-593 / Harvested from Project Euclid
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The maximal function along a curve $(t,\gamma(t),t\gamma(t))$ on the Heisenberg group is discussed. The $L\sp p$-boundedness of this operator is shown under the doubling condition of $\gamma\sp \prime$ for convex $\gamma$ in $\mathbb {R}\sp +$. This condition also applies to the singular integrals when $\gamma$ is extended as an even or odd function. The proof is based on angular Littlewood-Paley decompositions in the Heisenberg group.
Publié le : 2002-09-15
Classification:  42B20,  47G10 
@article{1087575457,
     author = {Kim, Joonil},
     title = {L<sup>
 p
</sup>-estimates for singular integrals and maximal operators
associated with flat curves on the Heisenberg group},
     journal = {Duke Math. J.},
     volume = {115},
     number = {1},
     year = {2002},
     pages = { 555-593},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087575457}
}

Kim, Joonil. L
 p
-estimates for singular integrals and maximal operators
associated with flat curves on the Heisenberg group. Duke Math. J., Tome 115 (2002) no. 1, pp.  555-593. http://gdmltest.u-ga.fr/item/1087575457/