$L^{p}$ type mapping estimates for oscillatory integrals in higher dimensions

• Autorzy: G. Sampson
• Języki publikacji: EN

Abstrakty

EN

We show in two dimensions that if $Kf = ∫_{ℝ₊²} k(x,y)f(y)dy$, $k(x,y) = (e^{ix^{a}·y^{b}})/(|x-y|^{η})$, p = 4/(2+η), a ≥ b ≥ 1̅ = (1,1), $v_{p}(y) = y^{(p/p')(1̅-b/a)}$, then $||Kf||_{p} ≤ C||f||_{p,v_{p}}$ if η + α₁ + α₂ < 2, $α_{j} = 1 - b_{j}/a_{j}$, j = 1,2. Our methods apply in all dimensions and also for more general kernels.

Kategorie tematyczne

• 47G10: Integral operators
• 46B70: Interpolation between normed linear spaces
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 172
• Numer: 2
• Strony: 101-123

Daty

wydano

2006

Twórcy

autor

G. Sampson

• Department of Mathematics, Auburn University, Auburn, AL 36849-5310, U.S.A.

Identyfikatory

DOI

10.4064/sm172-2-1