On approach regions for the conjugate Poisson integral and singular integrals

Ferrando, S.; Jones, R.; Reinhold, K.

Studia Mathematica, Tome 119 (1996), p. 169-182 / Harvested from The Polish Digital Mathematics Library

Résumé

Let ũ denote the conjugate Poisson integral of a function $f \in L^{p} (ℝ)$ . We give conditions on a region Ω so that $l i m_{(v, ε) \to (0, 0)} (v, ε) \in Ω ũ (x + v, ε) = H f (x)$ , the Hilbert transform of f at x, for a.e. x. We also consider more general Calderón-Zygmund singular integrals and give conditions on a set Ω so that $s u p_{(v, r) \in Ω} | ʃ_{| t | > r} k (x + v - t) f (t) d t |$ is a bounded operator on $L^{p}$ , 1 < p < ∞, and is weak (1,1).

Publié le : 1996-01-01

Zbl 0862.42011

EUDML-ID : urn:eudml:doc:216328

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     author = {S. Ferrando and R. Jones and K. Reinhold},
     title = {On approach regions for the conjugate Poisson integral and singular integrals},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {169-182},
     zbl = {0862.42011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv120i2p169bwm}
}

Ferrando, S.; Jones, R.; Reinhold, K. On approach regions for the conjugate Poisson integral and singular integrals. Studia Mathematica, Tome 119 (1996) pp. 169-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv120i2p169bwm/

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