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Weak spectral synthesis in Fourier algebras of coset spaces

Eberhard Kaniuth (2010)

Studia Mathematica

Let G be a locally compact group, K a compact subgroup of G and A(G/K) the Fourier algebra of the coset space G/K. Applying results from [E. Kaniuth, Weak spectral synthesis in commutative Banach algebras, J. Funct. Anal. 254 (2008), 987-1002], we establish injection and localization theorems relating weak spectral sets and weak Ditkin sets for A(G/K) to such sets for A(H/H ∩ K), where H is a closed subgroup of G. We also prove some results towards the analogue of Malliavin's theorem for weak spectral...

Weak type (1,1) multipliers on LCA groups

José Raposo (1997)

Studia Mathematica

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...

Weak type radial convolution operators on free groups

Tadeusz Pytlik, Ryszard Szwarc (2008)

Studia Mathematica

Radial convolution operators on free groups with nonnegative kernel of weak type (2,2) and of restricted weak type (2,2) are characterized. Estimates of weak type (p,p) are obtained as well for 1 < p < 2.

Weighted inequalities and the shape of approach regions

José García, Javier Soria (1999)

Studia Mathematica

We characterize geometric properties of a family of approach regions by means of analytic properties of the class of weights related to the boundedness of the maximal operator associated with this family.

Weighted measure algebras and uniform norms

S. J. Bhatt, H. V. Dedania (2006)

Studia Mathematica

Let ω be a weight on an LCA group G. Let M(G,ω) consist of the Radon measures μ on G such that ωμ is a regular complex Borel measure on G. It is proved that: (i) M(G,ω) is regular iff M(G,ω) has unique uniform norm property (UUNP) iff L¹(G,ω) has UUNP and G is discrete; (ii) M(G,ω) has a minimum uniform norm iff L¹(G,ω) has UUNP; (iii) M₀₀(G,ω) is regular iff M₀₀(G,ω) has UUNP iff L¹(G,ω) has UUNP, where M₀₀(G,ω) := {μ ∈ M(G,ω) : μ̂ = 0 on Δ(M(G,ω))∖Δ(L¹(G,ω))}.

Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

Sergio Antonio Tozoni (2004)

Studia Mathematica

Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis ( e j ) j ≥ 1 . Given an operator T from L c ∞ ( X ) to L¹(X), we consider the vector-valued extension T̃ of T given by T ̃ ( ∑ j f j e j ) = ∑ j T ( f j ) e j . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...

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