Weak type (1,1) multipliers on LCA groups

• Autorzy: Raposo José A
• Języki publikacji: EN

Abstrakty

EN

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

EN

weak type multipliers; maximal operators; vector inequalities

Kategorie tematyczne

• 43A32: Other transforms and operators of Fourier type

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 122
• Numer: 2
• Strony: 123-130

Daty

wydano

1997

otrzymano

1995-07-21

poprawiono

1996-08-05

Twórcy

autor

Raposo José A

• Dept. Matemàtica Aplicada i Anàlisi, Univ. de Barcelona, 08071 Barcelona, Spain

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.