Nonconvolution transforms with oscillating kernels that map $Ḃ_{1}^{0,1}$ into itself

Sampson, G.

Studia Mathematica, Tome 104 (1993), p. 1-44 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider operators of the form $(Ωf)(y) = ʃ_{-∞}^∞ Ω(y,u)f(u)du$ with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and $h ∈ L^∞$ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space $Ḃ^{0,1}_1$ (= B) into itself. In particular, all operators with $h(y) = e^{i|y|^a}$, a > 0, a ≠ 1, map B into itself.

Détail

Publié le : 1993-01-01

Zbl 0817.47043

EUDML-ID : urn:eudml:doc:216001

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