A note on Orlicz spaces
Wavelets with composite dilations.
Invariant systems of conjugate harmonic functions associated with compact Lie groups
Operators associated with representations of amenable groups singular integrals induced by ergodic flows, the rotation method and multipliers
On subharmonicity inequalities involving solutions of generalized Cauchy-Riemann equations
A kernel associated with certain multiply connected domains and its applications to factorization theorems
The boundedness of Calderón-Zygmund operators on the spaces F .
Calderón-Zygmund operators are generalizations of the singular integral operators introduced by Calderón and Zygmund in the fifties [CZ]. These singular integrals are principal value convolutions of the form Tf(x) = límε→0 ∫|x-y|>ε K(x-y) f(y) dy = p.v.K * f(x), where f belongs to some class of test functions.
Wavelets obtained by continuous deformations of the Haar wavelet.
One might obtain the impression, from the wavelet literature, that the class of orthogonal wavelets is divided into subclasses, like compactly supported ones on one side, band-limited ones on the other side. The main purpose of this work is to show that, in fact, the class of low-pass filters associated with reasonable (in the localization sense, not necessarily in the smooth sense) wavelets can be considered to be an infinite dimensional manifold that is arcwise connected. In particular, we show...
The φ-transform and wavelet characterizations of Herz-type spaces.
In this paper, the authors establish the phi-transform and wavelet characterizations for some Herz and Herz-type Hardy spaces by means of a local version of the discrete tent spaces at the origin.
Littlewood-Paley theory and ϵ-families of operators
Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform
We just published a paper showing that the properties of the shift invariant spaces, ⟨f⟩, generated by the translates by ℤⁿ of an f in L²(ℝⁿ) correspond to the properties of the spaces L²(𝕋ⁿ,p), where the weight p equals [f̂,f̂]. This correspondence helps us produce many new properties of the spaces ⟨f⟩. In this paper we extend this method to the case where the role of ℤⁿ is taken over by locally compact abelian groups G, L²(ℝⁿ) is replaced by a separable Hilbert space on which a unitary representation...
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