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Walsh-Marcinkiewicz means and Hardy spaces

Károly Nagy, George Tephnadze (2014)

Open Mathematics

The main aim of this paper is to investigate the Walsh-Marcinkiewicz means on the Hardy space H p, when 0 < p < 2/3. We define a weighted maximal operator of Walsh-Marcinkiewicz means and establish some of its properties. With its aid we provide a necessary and sufficient condition for convergence of the Walsh-Marcinkiewicz means in terms of modulus of continuity on the Hardy space H p, and prove a strong convergence theorem for the Walsh-Marcinkiewicz means.

Wavelet analysis of the multivariate fractional brownian motion

Jean-François Coeurjolly, Pierre-Olivier Amblard, Sophie Achard (2013)

ESAIM: Probability and Statistics

The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behaviour of the correlation, showing that if the analyzing wavelet has a sufficient number of null first order moments, the decomposition eliminates any possible long-range (inter)dependence. The cross-spectral...

Wavelet bases in L p ( ℝ )

Gustaf Gripenberg (1993)

Studia Mathematica

It is shown that an orthonormal wavelet basis for L 2 ( ℝ ) associated with a multiresolution is an unconditional basis for L p ( ℝ ) , 1 < p < ∞, provided the father wavelet is bounded and decays sufficiently rapidly at infinity.

Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes

M. Clausel, F. Roueff, M. S. Taqqu, C. Tudor (2014)

ESAIM: Probability and Statistics

We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long–memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener–Itô integral of order 2. This happens even if the original...

Wavelet frames for distributions; local and pointwise regularity

Hans Triebel (2003)

Studia Mathematica

This paper deals with wavelet frames for a large class of distributions on euclidean n-space, including all compactly supported distributions. These representations characterize the global, local, and pointwise regularity of the distribution considered.

Wavelet Sets in ...

X. Dai, D.R. Larson, D.M. Speegle (1997)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Wavelet techniques for pointwise regularity

Stéphane Jaffard (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Let E be a Banach (or quasi-Banach) space which is shift and scaling invariant (typically a homogeneous Besov or Sobolev space). We introduce a general definition of pointwise regularity associated with E , and denoted by C E α ( x 0 ) . We show how properties of E are transferred into properties of C E α ( x 0 ) . Applications are given in multifractal analysis.

Wavelet transform for functions with values in UMD spaces

Cornelia Kaiser, Lutz Weis (2008)

Studia Mathematica

We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.

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