Related papers: Recent progress of Littlewood-paley Theory with ch…
In this paper, we prove the boundedness of the multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces, then we give the boundedness and weak-type $L\log L$ estimates for the commutators of multilinear…
Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…
Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as $\mathbb{Z}_2$-involutions in the passive transformation on the spacetime coordinates; but together with a charge conjugation C, the total…
In this paper, we introduce a family of integral transforms, denoted by \(\mathcal{O}_{\alpha}\), and constructed via kernel fusion of the fractional Fourier transform (FRFT) with angle \(\alpha \notin \pi \mathbb{Z}\). We demonstrate that…
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental…
This paper consists of four parts. It begins by using the authors's generalized Schauder formula, [50], and the algebraic multiplicity, $\chi$, of Esquinas and L\'opez-G\'omez [18,17,40] to package and sharpening all existing results in…
Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…
We study a.e. convergence on $L^p$, and Lorentz spaces $L^{p,q}$, $p>\tfrac{2d}{d-1}$, for variants of Riesz means at the critical index $d(\tfrac 12-\tfrac 1p)-\tfrac12$. We derive more general results for (quasi-)radial Fourier…
We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$.…
We prove that for any $L^Q$-valued Schwartz function $f$ defined on $\mathbb{R}^d$, one has the multiple vector-valued, mixed norm estimate $$ \| f \|_{L^P(L^Q)} \lesssim \| S f \|_{L^P(L^Q)} $$ valid for every $d$-tuple $P$ and every…
Littlewood--Paley theory began with the classic paper of Littlewood and Paley (J.\ E.\ Littlewood, R.\ E.\ A.\ C.\ Paley, {\em Theorems on Fourier Series and Power Series}. J. Lond. Math. Soc. (1), {\bf 6} (1931), 230--33). We discuss this…
In this paper we prove a parabolic version of the Littlewood-Paley inequality for the operators of the type $\phi(-\Delta)$, where $\phi$ is a Bernstein function. As an application, we construct an $L_p$-theory for the stochastic…
Solution of some boundary value problems and initial problems in unique ball leads to the convergence and sumability problems of Fourier series of given function by eigenfunctions of Laplace operator on a sphere - spherical harmonics. Such…
Skewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutative symmetric functions is a useful tool for studying…
We obtain a characterisation of the Fourier transform on the space of Schwartz-Bruhat functions on locally compact Abelian groups. The result states that any appropriately additive bijection of the Schwartz space onto itself, which…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
Recently, a theoretical framework was set up in [1], which allows for the symmetry-preserving inclusion of full quark-gluon vertices in the description of the meson dynamics. In the present work, we develop a special truncation within this…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
Following a symmetrization procedure proposed recently by Nowak and Stempak, we consider the setting of symmetrized Jacobi expansions. In this framework we investigate mapping properties of several fundamental harmonic analysis operators,…
We develop a generalized Littlewood-Paley theory for semigroups acting on $L^p$-spaces of functions with values in uniformly convex or smooth Banach spaces. We characterize, in the vector-valued setting, the validity of the one-sided…