Related papers: A short proof of commutator estimates

In this paper, we initially derive the equivalent fractional integral equation to $\Psi$-Hilfer hybrid fractional differential equations and through it, we prove the existence of a solution in the weighted space. The primary objective of…

In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…

Shifted partial derivative (SPD) methods are a central algebraic tool for circuit lower bounds, measuring the dimension of spaces of shifted derivatives of a polynomial. We develop the Shifted Partial Derivative Polynomial (SPDP) framework,…

In this work we define a Fourier transform for each $f\in L^{p(\cdot)}(\mathbb{R})$, for a large class of exponent functions $p(\cdot)$, as the distributional derivative of a H\"older continuous function. A norm is defined in the space of…

This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…

In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from a work of Holmes, Rahm and Spencer. We give new proofs for those inequalities relying upon a…

Let $\mathcal{F}(\textbf{k},\mathfrak{q})$ be the set of primitive Hilbert modular forms of weight $\textbf{k}$ and prime level $\mathfrak{q}$, with trivial central character. We study the one-level density of low-lying zeros of $L(s,\pi)$…

There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have…

Fractional variation is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. Fractional velocity can be suitable for characterizing singular behavior of derivatives…

We consider the reduction of problems on general noncommutative $L_p$-spaces to the corresponding ones on those associated with finite von Neumann algebras. The main tool is a unpublished result of the first named author which approximates…

We obtain $L_p$ estimates for fractional parabolic equations with space-time non-local operators $$ \partial_t^\alpha u - Lu + \lambda u= f \quad \mathrm{in} \quad (0,T) \times \mathbb{R}^d,$$ where $\partial_t^\alpha u$ is the Caputo…

Using recent developments on locally compact groups, we are able to obtain quantitative results on embeddings into Lebesgue spaces for a large class of HNN extensions.

The purpose of this note is to point out a simple consequence of some earlier work of the authors, "Hard Sard: Quantitative implicit function and extension theorems for Lipschitz maps". For $f$, a Lipschitz function from a Euclidean space…

The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…

Let $p$ be a prime. We prove bounds on short Dirichlet character sums evaluated at a class of homogeneous polynomials in arbitrary dimensions. In every dimension, this bound is nontrivial for sums over boxes with side lengths as short as…

The $L^p$-cohomology in degree 1 of Riemannian homogeneous spaces is computed. It turns out that reduced cohomology does not vanish exactly for spaces quasiisometric to negatively curved homogeneous spaces.

Semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony. In this paper, we study a class of marginal partially linear quantile models with possibly varying…

Let $B^p_{\sigma}$, $1\le p<\infty$, $\sigma>0$, denote the space of all $f\in L^p(\mathbb{R})$ such that the Fourier transform of $f$ (in the sense of distributions) vanishes outside $[-\sigma,\sigma]$. The classical sampling theorem…

This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…

Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…