Weighted bounds for variational Fourier series

• Autorzy: Yen Do , Michael Lacey
• Języki publikacji: EN

Abstrakty

EN

For 1 < p < ∞ and for weight w in $A_{p}$, we show that the r-variation of the Fourier sums of any function f in $L^{p}(w)$ is finite a.e. for r larger than a finite constant depending on w and p. The fact that the variation exponent depends on w is necessary. This strengthens previous work of Hunt-Young and is a weighted extension of a variational Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses weighted adaptation of phase plane analysis and a weighted extension of a variational inequality of Lépingle.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 211
• Numer: 2
• Strony: 153-190

Daty

wydano

2012

Twórcy

autor

Yen Do

• Department of Mathematics, Yale University, New Haven, CT 06511, U.S.A.

autor

Michael Lacey

• School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

Identyfikatory

DOI

10.4064/sm211-2-4