Related papers: A weak type estimate for regular fractional sparse…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
In this paper, we first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional…
In this paper we present three types of Caputo-Hadamard derivatives of variable fractional order, and study the relations between them. An approximation formula for each fractional operator, using integer-order derivatives only, is…
In this article, we propose the fractional weak adversarial networks (f-WANs) for the stationary fractional advection dispersion equations (FADE) based on their weak formulas. This enables us to handle less regular solutions for the…
For any integer $n \geq 2$, we establish $L^p(\R^n)$ inequalities for the $r$-variations of Stein-Wainger type oscillatory integral operators with general phase functions. These inequalities closely related to Carleson's theorem are sharp,…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
We introduce a fractional magnetic pseudorelativistic operator for a general fractional order $s\in(0,1)$. First we define a suitable functional setting and we prove some fundamental properties. Then we show the behavior of the operator as…
Weak approximations have been developed to calculate the expectation value of functionals of stochastic differential equations, and various numerical discretization schemes (Euler, Milshtein) have been studied by many authors. We present a…
We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is…
There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study…
Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference…
In this article, we establish sharp weak endpoint estimates for $p$-adic fractional Hardy operator. In addition, sharp weak bounds for p-adic Hardy operator on p-adic central Morrey space are also obtained.
We obtain sharp estimates for the localized distribution function of M\phi, when \phi belongs to Lp,\inf where M is the dyadic maximal operator. We obtain these estimates given the L1 and Lq norm, q < p and certain weak Lp-conditions.
We present a new proof of the classical weak-type $(1,1)$ estimate for Calder\'on-Zygmund operators. This proof is inspired by ideas of Nazarov, Treil, and Volberg that address the non-doubling setting. An application to a weighted…
We develop a novel a posteriori error estimator for the $L^2$ error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization…
The notion of weakly separable extensions was introduced by N. Hamaguchi and A. Nakajima as a generalization of separable extensions. The purpose of this article is to give a characterization of weakly separable polynomials in skew…
It has been shown in literature that the Lasso estimator, or l1-penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the l1-penalty allow for sharp oracle results, and then…
Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the…
Lacey and Thiele have recently obtained a new proof of Carleson's theorem on almost everywhere convergence of Fourier series. This paper is a generalization of their techniques (known broadly as time-frequency analysis) to higher…
We consider the nonparametric regression and the classification problems for $\psi$-weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association, $\ldots$. A penalized estimation…