Do you want to publish a course? Click here

Fefferman-Stein inequalities for the mathbb{Z}_2^d Dunkl maximal operator

410   0   0.0 ( 0 )
 Added by Luc Deleaval
 Publication date 2013
  fields
and research's language is English
 Authors Luc Deleaval




Ask ChatGPT about the research

In this article, we establish the Fefferman-Stein inequalities for the Dunkl maximal operator associated with a finite reflection group generated by the sign changes. Similar results are also given for a large class of operators related to Dunkls analysis.



rate research

Read More

In this paper, we consider the Fefferman-Stein decomposition of $Q_{alpha}(mathbb{R}^{n})$ and give an affirmative answer to an open problem posed by M. Essen, S. Janson, L. Peng and J. Xiao in 2000. One of our main methods is to study the structure of the predual space of $Q_{alpha}(mathbb{R}^{n})$ by the micro-local quantities. This result indicates that the norm of the predual space of $Q_{alpha}(mathbb{R}^{n})$ depends on the micro-local structure in a self-correlation way.
86 - Robert Kesler 2018
We exhibit a range of $ell ^{p}(mathbb{Z}^d)$-improving properties for the discrete spherical maximal average in every dimension $dgeq 5$. The strategy used to show these improving properties is then adapted to establish sparse bounds, which extend the discrete maximal theorem of Magyar, Stein, and Wainger to weighted spaces. In particular, the sparse bounds imply that the discrete spherical maximal average is a bounded map from $ell^2(w)$ into $ell^2(w)$ provided $w^{frac{d}{d-4}+delta}$ belongs to the Muckenhoupt class $A_2$ for some $delta>0.$
75 - Robert Kesler 2018
We prove an expanded range of $ell ^{p}(mathbb{Z}^d)$-improving properties and sparse bounds for discrete spherical maximal means in every dimension $dgeq 6$. Essential elements of the proofs are bounds for high exponent averages of Ramanujan and restricted Kloosterman sums.
Let $Dinmathbb{N}$, $qin[2,infty)$ and $(mathbb{R}^D,|cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, via an auxiliary function space $mathrm{WE}^{1,,q}(mathbb R^D)$ defined via wavelet expansions, the authors establish the Riesz transform characterization of Triebel-Lizorkin spaces $dot{F}^0_{1,,q}(mathbb{R}^D)$. As a consequence, the authors obtain the Fefferman-Stein decomposition of Triebel-Lizorkin spaces $dot{F}^0_{infty,,q}(mathbb{R}^D)$. Finally, the authors give an explicit example to show that $dot{F}^0_{1,,q}(mathbb{R}^D)$ is strictly contained in $mathrm{WE}^{1,,q}(mathbb{R}^D)$ and, by duality, $mathrm{WE}^{infty,,q}(mathbb{R}^D)$ is strictly contained in $dot{F}^0_{infty,,q}(mathbb{R}^D)$. Although all results when $D=1$ were obtained by C.-C. Lin et al. [Michigan Math. J. 62 (2013), 691-703], as was pointed out by C.-C. Lin et al., the approach used in the case $D=1$ can not be applied to the case $Dge2$, which needs some new skills.
The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a stochastic model: signals are tempered distributions such that the application of a whitening (differential) operator results in a realization of a sparse white noise. Using wavelets constructed from these operators, the sparsity of the white noise can be inherited by the wavelet coefficients. In this paper, we specify such wavelets in full generality and determine their properties in terms of the underlying operator.
comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا