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C. J. Neugebauer (2009)
Studia Mathematica
Let be the Ariõ-Muckenhoupt weight class which controls the weighted -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated -norm inequalities of the Hardy operator.
Dashan Fan, Shuichi Sato (2004)
Studia Mathematica
We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
Hugo Aimar, Liliana Forzani (1991)
Studia Mathematica
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.
Alexander Stokolos (2005)
Annales de l’institut Fourier
We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies a weak type estimate. This allows us to complete Zygmund’s program of the description of the translation invariant bases of multidimensional intervals in the particular case of products of two cubic intervals. As a conjecture, we suggest a more precise version of Zygmund’s program.
Fu, Zun-Wei (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Е.И. Бережной (1995)
Sibirskij matematiceskij zurnal
Э.Н. Батуев, В.Д. Степанов (1989)
Sibirskij matematiceskij zurnal
В.Ю. Шелепов (1987)
Matematiceskij sbornik
А. Янушаускас (1971)
Sibirskij matematiceskij zurnal
Н.Я. Крупник, В.И. Няга (1975)
Matematiceskie issledovanija
M.M. Скриганов (1996)
Zapiski naucnych seminarov POMI
И.Ф. Панченко (1976)
Matematiceskie issledovanija
Л.Г. Гуров (1994)
Sibirskij matematiceskij zurnal
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