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Wenchang Sun

Publications and source records attributed to Wenchang Sun.

30 records · Page 2Linked to original sources
arXiv2017

Local and Global Phaseless Sampling in Real Spline Spaces

We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on the whole line from infinitely many unsigned samples. In both cases, we give characterizations for a sequence of distinct points to be a phaseless sampling sequence, at which any nonseparable function is determined up to a sign on an interval or on the whole line by its unsigned sampled values. Moreover, for the case of local recovery, we also study the almost phaseless sampling and give a necessary and sufficient condition for a sequence of points to admit local recovery for almost all functions.

math.FA↗
arXiv2014

Multilinear Fourier multipliers on variable Lebesgue spaces

In this paper, we study properties of the bilinear multiplier space. We give a necessary condition for a continuous integrable function to be a bilinear multiplier on variable exponent Lebesgue spaces. And we prove the localization theorem of multipliers on variable exponent Lebesgue spaces. Moreover, we present a Mihlin-Hörmander type theorem for multilinear Fourier multipliers on weighted variable Lebesgue spaces and give some applications.

math.CA↗
arXiv2014

Two weight norm inequalities for the bilinear fractional integrals

In this paper, we give a characterization of the two weight strong and weak type norm inequalities for the bilinear fractional integrals. Namely, we give the characterization of the following inequalities, \[ \|\mathcal I_α(f_1σ_1, f_2σ_2)\|_{L^q(w)} \le \mathscr N \prod_{i=1}^2\|f_i\|_{L^{p_i}(σ_i)} \] and \[ \|\mathcal I_α(f_1σ_1, f_2σ_2)\|_{L^{q,\infty}(w)} \le \mathscr N_{\textup{weak}} \prod_{i=1}^2\|f_i\|_{L^{p_i}(σ_i)}, \] when $q\ge p_1, p_2>1$ and $p_1+p_2\ge p_1p_2$.

math.CA↗
arXiv2013

The sharp weighted bound for multilinear maximal functions and Calderón-Zygmund operators

We investigate the weighted bounds for multilinear maximal functions and Calderón-Zygmund operators from $L^{p_1}(w_1)\times...\times L^{p_m}(w_m)$ to $L^{p}(v_{\vec{w}})$, where $1<p_1,...,p_m<\infty$ with $1/{p_1}+...+1/{p_m}=1/p$ and $\vec{w}$ is a multiple $A_{\vec{P}}$ weight. We prove the sharp bound for the multilinear maximal function for all such $p_1,..., p_m$ and prove the sharp bound for $m$-linear Calderón-Zymund operators when $p\geq 1$.

math.CA↗
arXiv2013

Calderón-Zygmund Operators with Non-diagonal Singularity

In this paper, we introduce a class of singular integral operators which generalize Calderón-Zygmund operators to the more general case, where the set of singular points of the kernel need not to be the diagonal, but instead, it can be a general hyper curve. We show that such operators have similar properties as ordinary Calderón-Zygmund operators. In particular, we prove that they are of weak-type $(1, 1)$ and strong type $(p,p)$ for $1<p<\infty$.

math.CA↗
arXiv2012

Weak and Strong Type Weighted Estimates for Multilinear Calderón-Zygmund Operators

In this paper, we study the weighted estimates for multilinear Calderón-Zygmund operators %with multiple $A_{\vec{P}}$ weights from $L^{p_1}(w_1)\times...\times L^{p_m}(w_m)$ to $L^{p}(v_{\vec{w}})$, where $1<p, p_1,...,p_m<\infty$ with $1/{p_1}+...+1/{p_m}=1/p$ and $\vec{w}=(w_1,...,w_m)$ is a multiple $A_{\vec{P}}$ weight. We give weak and strong type weighted estimates of mixed $A_p$-$A_\infty$ type. Moreover, the strong type weighted estimate is sharp whenever $\max_i p_i \le p'/(mp-1)$.

math.CA↗
arXiv2011

Inversion Formula for the Windowed Fourier Transform

In this paper, we study the inversion formula for recovering a function from its windowed Fourier transform. We give a rigorous proof for an inversion formula which is known in engineering. We show that the integral involved in the formula is convergent almost everywhere on $\bbR$ as well as in $L^p$ for all $1<p<\infty$ if the function to be reconstructed is.

math.FA↗
arXiv2010

A New Formula for the Inverse Wavelet Transform

Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.

math.FA↗
arXiv2005

G-frames and G-Riesz Bases

G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients. We give characterizations of g-frames and prove that g-frames share many useful properties with frames. We also give generalized version of Riesz bases and orthonormal bases. As an application, we get atomic resolutions for bounded linear operators.

math.FA↗