$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains

• Autorzy: Yibiao Pan , Gary Sampson , Paweł Szeptycki
• Języki publikacji: EN

Abstrakty

EN

We prove the $L^p$ boundedness of certain nonconvolutional oscillatory integral operators and give explicit description of their extended domains. The class of phase functions considered here includes the function $|x|^{α}|y|^{β}$. Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.

Słowa kluczowe

EN

$L^p$ boundedness; oscillatory integrals; extended domains; Calderón-Zygmund kernels

Kategorie tematyczne

• 47G10: Integral operators
• 42A50: Conjugate functions, conjugate series, singular integrals
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 122
• Numer: 3
• Strony: 201-224

Daty

wydano

1997

otrzymano

1995-07-24

poprawiono

1996-07-24

Twórcy

autor

Yibiao Pan

• Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.

autor

Gary Sampson

• Department of Mathematics, Auburn University, Auburn, Alabama 36849, U.S.A.

autor

Paweł Szeptycki

• Department of Mathematics, University of Kansas Lawrence, Kansas 66044, U.S.A.

Bibliografia

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