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On approach regions for the conjugate Poisson integral and singular integrals

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

Studia Mathematica

1996

tom 120

nr 2

169-182

Let ũ denote the conjugate Poisson integral of a function $f ∈ L^{p}(ℝ)$. We give conditions on a region Ω so that $lim_{(v,ε)→(0,0)}_{(v,ε)∈Ω} ũ(x+v,ε) = Hf(x)$, 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 $sup_{(v,r)∈Ω} |ʃ_{|t|>r} k(x+v-t)f(t)dt|$ is a bounded operator on $L^p$, 1 < p < ∞, and is weak (1,1).

Ograniczanie wyników

1 Studia Mathematica

1 Ferrando S.

1 Jones R. L.

1 Reinhold K.

1 1996

Wyniki wyszukiwania

On approach regions for the conjugate Poisson integral and singular integrals