Related papers: Simplified Inequalities for Fractional Wavelet Fra…

Affine fractional Lp Polya-Szego inequalities for two functions on R^n are established, which are stronger than the Euclidean fractional Lp Polya-Szego inequalities.

This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet…

In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…

We consider representations of Cuntz--Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these representations and the associated Perron-Frobenius…

We prove three results on wavelets for the Hardy space H^2(\R). All wavelets constructed so far for H^2(\R) are MSF wavelets. We construct a family of H^2-wavelets which are not MSF. An equivalence relation on H^2-wavelets is introduced and…

We consider a fractional elliptic equation in an unbounded set with both Dirichlet and fractional normal derivative datum prescribed. We prove that the domain and the solution are necessarily radially symmetric. The extension of the result…

The most fundamental notion for Hilbert space frames is the sequence of frame coefficients for a vector x in the space. Yet, we know little about the distribution of these coefficient sequences. In this paper, we make the first detailed…

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.

A known general program, designed to endow the quotient space ${\cal U}_{\cal A} / {\cal U}_{\cal B}$ of the unitary groups ${\cal U}_{\cal A}$, ${\cal U}_{\cal B}$ of the C$^*$ algebras ${\cal B}\subset{\cal A}$ with an invariant Finsler…

In the present work we consider the electromagnetic wave equation in terms of the fractional derivative of the Caputo type. The order of the derivative being considered is 0 <\gamma<1. A new parameter \sigma, is introduced which…

We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L^2 function, a given likelihood function has an alternative representation as a product of…

In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities over bounded domains for the centered fractional maximal function and the fractional integral operator.

We present Hilbert space representation for a relatively broad class of minimum-length deformed quantum mechanical models obtained by incorporating a space-time uncertainty relation into quantum mechanics. The correspondingly modified field…

We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations.

Sharp affine fractional $L^p$ Sobolev inequalities for functions on $\mathbb R^n$ are established. The new inequalities are stronger than (and directly imply) the sharp fractional $L^p$ Sobolev inequalities. They are fractional versions of…

We survey some recent regularity results for fractional p-Laplacian elliptic equations, especially focusing on pure and weighted boundary H\"older continuity of the solutions of related Dirichlet problems. Then, we present some applications…

It is proved that given $-1/2<s<1/2$, for any $f\in L^2(\mathbb{R})$, there is a unique $u\in \widehat{H}^{|s|}(\mathbb{R})$ such that $$ f=\boldsymbol{D}^{-s}u+\boldsymbol{D}^{s*}u\,, $$ where $\boldsymbol{D}^{-s}, \boldsymbol{D}^{s*}$ are…

We obtain subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces embedded in $\mathbb{C}^n$ with isolated singularities. $W^{\epsilon}$ Sobolev norms of a form, $f$, for $0< \epsilon < 1$ are estimated in terms…

We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations with a drift.

We give ground-state representation for the fractional Laplacian with Dirichlet condition on the half-line