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Gabor meets Littlewood-Paley: Gabor expansions in L p ( d )

Karlheinz Gröchenig, Christopher Heil (2001)

Studia Mathematica

It is known that Gabor expansions do not converge unconditionally in L p and that L p cannot be characterized in terms of the magnitudes of Gabor coefficients. By using a combination of Littlewood-Paley and Gabor theory, we show that L p can nevertheless be characterized in terms of Gabor expansions, and that the partial sums of Gabor expansions converge in L p -norm.

Gagliardo-Nirenberg inequalities in weighted Orlicz spaces

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2006)

Studia Mathematica

We derive inequalities of Gagliardo-Nirenberg type in weighted Orlicz spaces on ℝⁿ, for maximal functions of derivatives and for the derivatives themselves. This is done by an application of pointwise interpolation inequalities obtained previously by the first author and of Muckenhoupt-Bloom-Kerman-type theorems for maximal functions.

Generalized Besov type spaces on the Laguerre hypergroup

Miloud Assal, Hacen Ben Abdallah (2005)

Annales mathématiques Blaise Pascal

In this paper we study generalized Besov type spaces on the Laguerre hypergroup and we give some characterizations using different equivalent norms which allows to reach results of completeness, continuous embeddings and density of some subspaces. A generalized Calderón-Zygmund formula adapted to the harmonic analysis on the Laguerre Hypergroup is obtained inducing two more equivalent norms.

Generalized Hörmander conditions and weighted endpoint estimates

María Lorente, José María Martell, Carlos Pérez, María Silvina Riveros (2009)

Studia Mathematica

We consider two-weight estimates for singular integral operators and their commutators with bounded mean oscillation functions. Hörmander type conditions in the scale of Orlicz spaces are assumed on the kernels. We prove weighted weak-type estimates for pairs of weights (u,Su) where u is an arbitrary nonnegative function and S is a maximal operator depending on the smoothness of the kernel. We also obtain sufficient conditions on a pair of weights (u,v) for the operators to be bounded from L p ( v ) to...

Geometric Fourier analysis

Antonio Cordoba (1982)

Annales de l'institut Fourier

In this paper we continue the study of the Fourier transform on R n , n 2 , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of log ( N ) , where N is the number of equal angles considered in R 2 . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of R n , n 2 , of fixed eccentricity...

Good-λ inequalities for wavelets of compact support

Sarah V. Cook (2004)

Colloquium Mathematicae

For a wavelet ψ of compact support, we define a square function S w and a maximal function NΛ. We then obtain the L p equivalence of these functions for 0 < p < ∞. We show this equivalence by using good-λ inequalities.

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