Weighted weak type inequalities for certain maximal functions

• Autorzy: Hugo Aimar , Liliana Forzani
• Języki publikacji: EN

Abstrakty

EN

We give an A_p type characterization for the pairs of weights (w,v) for which the maximal operator Mf(y) = sup 1/(b-a) ʃ_a^b |f(x)|dx, where the supremum is taken over all intervals [a,b] such that 0 ≤ a ≤ y ≤ b/ψ(b-a), is of weak type (p,p) with weights (w,v). Here ψ is a nonincreasing function such that ψ(0) = 1 and ψ(∞) = 0.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991-1992
• Tom: 101
• Numer: 1
• Strony: 105-111

Daty

wydano

1991

otrzymano

1991-02-07

Twórcy

autor

Hugo Aimar

• Programa Especial de Matemática Aplicada, Intec-Conicet, C.C. NRO 91, 3000 Santa Fe, Argentina

autor

Liliana Forzani

• Departamento de Matemática, Facultad de Ingenieria Química-UNL, SGO. Del Estero 2829, 3000 Santa Fe, Argentina

Bibliografia

• [C] C. P. Calderón, Some remarks on the multiple Weierstrass transform and Abel summability of multiple Fourier-Hermite Series, Studia Math. 32 (1969), 119-148.
• [M1] B. Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139 (1969), 231-242.
• [M2] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, ibid. 165 (1972), 207-226.