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On the maximal function for rotation invariant measures in $ℝ^{n}$

100%

Vargas A. M.

Studia Mathematica

1994

tom 110

nr 1

9-17

Given a positive measure μ in $ℝ^n$, there is a natural variant of the noncentered Hardy-Littlewood maximal operator $M_{μ}f(x) = sup_{x ∈ B} 1/μ(B) ʃ_{B} |f|dμ$, where the supremum is taken over all balls containing the point x. In this paper we restrict our attention to rotation invariant, strictly positive measures μ in $ℝ^n$. We give some necessary and sufficient conditions for $M_μ$ to be bounded from $L^{1}(dμ)$ to $L^{1,∞}(dμ)$.

Weak type (1,1) multipliers on LCA groups

80%

Raposo J. A.

Studia Mathematica

1997

tom 122

nr 2

123-130

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.

Discrete Hardy spaces

80%

Boza S., Carro M. J.

Studia Mathematica

1998

tom 129

nr 1

31-50

We study various characterizations of the Hardy spaces $H^p(ℤ)$ via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of $H^p(ℤ)$ given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.

Ograniczanie wyników

3 Studia Mathematica

1 Boza S.

1 Carro M. J.

1 Raposo J. A.

1 Vargas A. M.

1 1998

1 1997

1 1994

Wyniki wyszukiwania

On the maximal function for rotation invariant measures in $ℝ^{n}$

Weak type (1,1) multipliers on LCA groups

Discrete Hardy spaces