This note significantly extends various earlier results concerning Fourier multipliers of modulation spaces. It combines not so widely known characterizations of pointwise multipliers of Wiener amalgam spaces with nov...
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This note significantly extends various earlier results concerning Fourier multipliers of modulation spaces. It combines not so widely known characterizations of pointwise multipliers of Wiener amalgam spaces with novel geometric ideas and a new approach to piecewise linear functions belonging to the Fourier algebra. Thus the paper provides two original types of results. On the one hand we establish results for step functions (i.e. piecewise constant, bounded functions), which are multipliers on the modulation spaces (M-omega(p,q)(R-d),||center dot||(p,q)(M omega)) with 1modulation space M-1(R-d), also known as the Segal algebra S-0(R-d) (see [6] and [25]). (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).
We obtain the local well-posedness for Dirac equations with a Hartree type nonlinearity derived by decoupling the Dirac-Klein-Gordon system. We extend the function space of initial data, enabling us to handle initial ...
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We obtain the local well-posedness for Dirac equations with a Hartree type nonlinearity derived by decoupling the Dirac-Klein-Gordon system. We extend the function space of initial data, enabling us to handle initial data that were not addressed in previous studies.
This paper is devoted to the study of the initial value problem for a nonlinear plate equation in Rnx(0,infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag...
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This paper is devoted to the study of the initial value problem for a nonlinear plate equation in Rnx(0,infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>n\times (0,\infty )$$\end{document} with initial data in modulation spaces, which includes the Bessel-potential Hps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H<^>{s}_p$$\end{document} and Besov spaces Bp,qs,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B<^>{s}_{p,q},$$\end{document} for large regularity indexes s. We derive a set of time-decay estimates for the corresponding linear plate equation on the framework of modulation spaces, and then, we use these results to analyze the existence and asymptotic stability of global solutions of the nonlinear problem.
We consider the initial value problem (IVP) associated with a higher order non-linear Schr & ouml;dinger (h-NLS) equation partial derivative tu+ia partial derivative x2u+b partial derivative x3u=2ia|u|2u+6b|u|2 pa...
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We consider the initial value problem (IVP) associated with a higher order non-linear Schr & ouml;dinger (h-NLS) equation partial derivative tu+ia partial derivative x2u+b partial derivative x3u=2ia|u|2u+6b|u|2 partial derivative xu,x,t is an element of R,with given data in the modulation space Ms2,p(R). Using ideas from Killip, Visan, Zhang, Oh and Wang, we prove that the IVP associated with the h-NLS equation is globally well-posed in the modulation spaces Ms2,p(R) for s >= 14 and p >= 2. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining. AI training and similar technologies
We consider the global well-posedness in modulation spaces and scaling limit modulation spaces under smallness assumption on the initial data for the coupled generalized KdV-KdV (gKdV) system. Moreover, we prove a H1$...
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We consider the global well-posedness in modulation spaces and scaling limit modulation spaces under smallness assumption on the initial data for the coupled generalized KdV-KdV (gKdV) system. Moreover, we prove a H1$$ {H}<^>1 $$ scattering criterion for the system.
We study the Cauchy problem for Hartree equation with cubic convolution nonlinearity F(u) = (k * vertical bar u vertical bar(2)) u under a specified condition on potential k with Cauchy data in modulation spaces M-p,M...
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We study the Cauchy problem for Hartree equation with cubic convolution nonlinearity F(u) = (k * vertical bar u vertical bar(2)) u under a specified condition on potential k with Cauchy data in modulation spaces M-p,M-q(R-n). We establish global well- posedness results in M-p,M-p(R-n) with 1 <= p < 2n/n+v, when k(x) = lambda/vertical bar x vertical bar(v) (lambda is an element of R, 0 < v < min{2, n/2});in M-p,M-q(R-n) with 1 <= q <= p <= 2, when k is an element of M-infinity,M-1(R-n). (C) 2017 Elsevier Ltd. All rights reserved.
We indicate how to construct a family of modulation spaces that have a scaling symmetry. We also illustrate the behavior of the Schrodinger multiplier on such function spaces. (C) 2019 The Authors. Published by Elsevi...
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We indicate how to construct a family of modulation spaces that have a scaling symmetry. We also illustrate the behavior of the Schrodinger multiplier on such function spaces. (C) 2019 The Authors. Published by Elsevier Inc.
We identify the generalised modulation spaces associated with tensor products of amalgam spaces having a large class of Banach spaces as their local component. As consequences of the main results, we describe the modu...
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We identify the generalised modulation spaces associated with tensor products of amalgam spaces having a large class of Banach spaces as their local component. As consequences of the main results, we describe the modulation spaces associated with tensor products of various L-p spaces.
We study the local-in-time regularity of the Brownian motion with respect to localized variants of modulation spaces M-s(p,q) and Wiener amalgam spaces W-s(p,q). We show that the periodic Brownian motion belongs local...
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We study the local-in-time regularity of the Brownian motion with respect to localized variants of modulation spaces M-s(p,q) and Wiener amalgam spaces W-s(p,q). We show that the periodic Brownian motion belongs locally in time to Ms-p,Ms-q (T) and W-s(p,q) (T) for (s - 1)q < -1, and the condition on the indices is optimal. Moreover, with the Wiener measure mu on T, we show that (M-s(p,q) (T), mu) and (W-s(p,q) (T), mu) form abstract Wiener spaces for the same range of indices, yielding large deviation estimates. We also establish the endpoint regularity of the periodic Brownian motion with respect to a Besov-type space (b) over cap (s)(p,infinity)(T). Specifically, we prove that the Brownian motion belongs to (b) over cap (s)(p,infinity)(T) for (s - 1) p = -1, and it obeys a large deviation estimate. Finally, we revisit the regularity of Brownian motion on usual local Besov spaces B-p,q(s), and indicate the endpoint large deviation estimates. (C) 2011 Elsevier Inc. All rights reserved.
We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especial...
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We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especially, we establish the analogue of the sharp Sobolev embedding theorem on weighted modulation spaces.
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