On the characterization of Hardy-Besov spaces on the dyadic group and its applications

• Autorzy: Jun Tateoka
• Języki publikacji: EN

Abstrakty

EN

C. Watari [12] obtained a simple characterization of Lipschitz classes $Lip^{(p)}α(W) (1 ≥ p ≥ ∞, α > 0)$ on the dyadic group using the $L^p$-modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces $B^α_{p,q}$ on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces $B^α_{p,q}$ by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality of the type of the Maz'ya inequality, a weak type estimate for maximal Cesàro means and a sufficient condition of absolute convergence of Walsh-Fourier series.

Kategorie tematyczne

• 43A75: Analysis on specific compact groups
• 26A16: Lipschitz (H\"older) classes
• 41A25: Rate of convergence, degree of approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 110
• Numer: 2
• Strony: 127-148

Daty

wydano

1994

poprawiono

1993-06-09

Twórcy

autor

Jun Tateoka

• Department of Mathematics, Akita University, Tegata, Akita 010, Japan

Bibliografia

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