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A pointwise estimate for pseudo-differential operators
Bulletin of Mathematical Sciences, 2023 Let [Formula: see text] be a pseudo-differential operator defined by the symbol [Formula: see text] with [Formula: see text] [Formula: see text]. It is shown that if [Formula: see text], then the operator satisfies the following pointwise estimate: (Tau)♯
Guangqing Wang, Wenyi Chen
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On L 2 $L^{2}$ -boundedness of Fourier integral operators
Journal of Inequalities and Applications, 2020 Let T a , φ $T_{a,\varphi }$ be a Fourier integral operator with symbol a and phase φ. In this paper, under the conditions a ( x , ξ ) ∈ L ∞ S ρ n ( ρ − 1 ) / 2 ( ω ) $a(x,\xi )\in L^{\infty }S^{n(\rho -1)/2}_{\rho }(\omega )$ and φ ∈ L ∞ Φ 2 $\varphi ...
Jie Yang, Wenyi Chen, Jiang Zhou
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AIMS Mathematics, 2022 In this paper we introduce an efficient and new numerical algorithm for evaluating a pseudo differential operator. The proposed algorithm is time saving and fruitful.
Amit K. Pandey +5 more
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Application of the Littlewood-Paley method to Calderon-Zygmund operators [PDF]
Surveys in Mathematics and its Applications, 2022 In this article, we establish the conditions for the pseudo-differential operator T under which this operator can be represented in convolution form with the singular kernel that satisfies |∂ xα ∂ zβ k(x,z)| ≤ Aβα(L)|z|-l-m-|β |-L for all z ≠ 0, and all ...
Mykola Yaremenko
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A conservative exponential integrators method for fractional conservative differential equations
AIMS Mathematics, 2023 The paper constructs a conservative Fourier pseudo-spectral scheme for some conservative fractional partial differential equations. The scheme is obtained by using the exponential time difference averaged vector field method to approximate the time ...
Yayun Fu , Mengyue Shi
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Journal of Inequalities and Applications, 2009 We study the existence and uniqueness of almost automorphic (resp., pseudo-almost automorphic) solutions to a first-order differential equation with linear part dominated by a Hille-Yosida type operator with nondense domain.
Bruno de Andrade, Claudio Cuevas
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Pseudo-differential operators and equations in a discrete half-space
Mathematical Modelling and Analysis, 2018 We introduce a digital pseudo-differential operator acting in discrete Sobolev--Slobodetskii spaces and consider pseudo-differential equations with such operators in a discrete half-space.
Alexander V. Vasilyev +1 more
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Karpatsʹkì Matematičnì Publìkacìï, 2015 A fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric $\alpha$-stable process in multidimensional Euclidean space. Its generator $\mathbf{A}$ is a
M.M. Osypchuk
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Математичні Студії, 2021 This article is aimed at determining existence conditions of single layer potentials for pseudo-differential equations related to some linear transformations of a rotationally invariant stable stochastic process in a multidimensional Euclidean space and ...
Kh. V. Mamalyha, M. M. Osypchuk
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Karpatsʹkì Matematičnì Publìkacìï, 2019 In this article an arbitrary invertible linear transformations of a symmetric $\alpha$-stable stochastic process in $d$-dimensional Euclidean space $\mathbb{R}^d$ are investigated.
Kh.V. Mamalyha, M.M. Osypchuk
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