Power means and the reverse Hölder inequality

• Autorzy: Victor D. Didenko , Anatolii A. Korenovskyi
• Języki publikacji: EN

Abstrakty

EN

Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Hölder inequality with exponents 0 < α < β. In the present paper, sharp estimates of the compositions of the power means $𝓟_{α}w(x): = ((1/x) ∫_{0}^{x} w^{α}(t)dt)^{1/α}$, x > 0, are obtained for various exponents α. As a result, for the function w a property of self-improvement of summability exponents is established.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 207
• Numer: 1
• Strony: 85-95

Daty

wydano

2011

Twórcy

autor

Victor D. Didenko

• University of Brunei Darussalam, BE1410 Bandar Seri Begawan, Brunei

autor

Anatolii A. Korenovskyi

• Odessa I. I. Mechnikov National University, Dvoryanskaya 2, 65026 Odessa, Ukraine

Identyfikatory

DOI

10.4064/sm207-1-6