On $L_{p} - L_{q}$ boundedness for convolutions with kernels having singularities on a sphere

• Autorzy: Alexey N. Karapetyants
• Języki publikacji: EN

Abstrakty

EN

For the convolution operators $A_{a}^{α}$ with symbols $a(|ξ|)|ξ|^{-α} exp{i|ξ|}$, 0 ≤ Re α < n, $a(|ξ|) ∈ L_{∞}$, we construct integral representations and give the exact description of the set of pairs (1/p,1/q) for which the operators are bounded from $L_{p}$ to $L_{q}$.

Kategorie tematyczne

• 42B15: Multipliers
• 31B10: Integral representations, integral operators, integral equations methods
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 44A35: Convolution

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 144
• Numer: 2
• Strony: 121-134

Daty

wydano

2001

Twórcy

autor

Alexey N. Karapetyants

• Mathematics Department, Center for Research and Advanced Study, A.P. 14-740, 07000 México, D.F., México

Identyfikatory

DOI

10.4064/sm144-2-2