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Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

Ferenc Weisz (1996)

Studia Mathematica

The martingale Hardy space H p ( [ 0 , 1 ) 2 ) and the classical Hardy space H p ( 2 ) are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from H p to L p (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a...

Strong summability of Ciesielski-Fourier series

Ferenc Weisz (2004)

Studia Mathematica

A strong summability result is proved for the Ciesielski-Fourier series of integrable functions. It is also shown that the strong maximal operator is of weak type (1,1).

Sufficient conditions for the spectrality of self-affine measures with prime determinant

Jian-Lin Li (2014)

Studia Mathematica

Let μ M , D be a self-affine measure associated with an expanding matrix M and a finite digit set D. We study the spectrality of μ M , D when |det(M)| = |D| = p is a prime. We obtain several new sufficient conditions on M and D for μ M , D to be a spectral measure with lattice spectrum. As an application, we present some properties of the digit sets of integral self-affine tiles, which are connected with a conjecture of Lagarias and Wang.

Sur le diamètre transfini entier d'un intervalle réel

Francesco Amoroso (1990)

Annales de l'institut Fourier

En utilisant à la fois la théorie des polynômes orthogonaux et des arguments élémentaires de géométrie des nombres, nous donnons ici des nouveaux encadrements pour le diamètre transfini entier d’un intervalle I d’extrémités rationnelles. Ces encadrements dépendent explicitement de la longueur de I et des dénominateurs de ses extrémités.

Sur l'existence des analyses multi-résolutions en théorie des ondelettes.

Pierre Gilles Lemarie-Rieusset (1992)

Revista Matemática Iberoamericana

On montre qu'une base d'ondelettes (ψj,k) de L2(R) avec une fonction mère ψ höldérienne à support compact provient nécessairement d'une analyse multi-résolution. La fonction-père φ a alors la même régularité que la fonction ψ et peut être choisie à support compact.

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