Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
In [ABB] Asmar, Berkson and Bourgain prove that for a sequence ${ϕ_j}^∞_{j=1} $ of weak type (1, 1) multipliers in $ℝ^n$ and a function $k ∈ L^1(ℝ^n)$ the weak type (1,1) constant of the maximal operator associated with ${k⁎ϕ_j}_j$ is controlled by that of the maximal operator associated with ${ϕ_j}_j$. In [ABG] this theorem is extended to LCA groups with an extra hypothesis: the multipliers must be continuous. In this paper we prove a more general version of this last result without assuming the continuity of the multipliers. The proof arises after simplifying the one in [ABB] which becomes then extensible to LCA groups.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
123-130
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-07-21
poprawiono
1996-08-05
Twórcy
autor
- Dept. Matemàtica Aplicada i Anàlisi, Univ. de Barcelona, 08071 Barcelona, Spain , raposo@cerber.mat.ub.es
Bibliografia
- [ABB] N. Asmar, E. Berkson and J. Bourgain, Restrictions from $ℝ^n$ to $ℤ^n$ of weak type (1, 1) multipliers, Studia Math. 108 (1994), 291-299.
- [ABG] N. Asmar, E. Berkson and T. A. Gillespie, Convolution estimates and generalized de Leuw Theorems for multipliers of weak type (1, 1), Canad. J. Math. 47 (1995), 225-245.
- [GR] J. García Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 46, North-Holland, 1985.
- [Ru] W. Rudin, Fourier Analysis on Groups, Wiley, 1990.
- [Sk] S. B. Stechkin, On the best lacunary systems of functions, Izv. Akad. Nauk SSSR 25 (1961), 357-366 (in Russian).
- [Sz] S. J. Szarek, On the best constants in the Khinchin inequality, Studia Math. 58 (1976), 197-208.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv122i2p123bwm