Results 31 to 40 of about 131 (87)
Modulation spaces Mp,q for 0 < p, q?8
Journal of Function Spaces, Volume 4, Issue 3, Page 329-341, 2006., 2006 The purpose of this paper is to construct modulation spaces Mp,q(Rd) for general 0 < p, q?8, which coincide with the usual modulation spaces when 1?p,q?8, and study their basic properties including their completeness. Given any g?S(Rd) such that supp g ???{?||?|?1} and ?k?Zd g (?-ak)=1, our modulation space consists of all tempered distributions f such
Masaharu Kobayashi, Hans Triebel
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Characterization of Riesz and Bessel potentials on variable Lebesgue spaces
Journal of Function Spaces, Volume 4, Issue 2, Page 113-144, 2006., 2006 Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that the exponent satisfies natural regularity conditions. As a consequence of this characterization, we
Alexandre Almeida +2 more
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Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz‐Sobolev embeddings
Journal of Function Spaces, Volume 3, Issue 2, Page 183-208, 2005., 2005 Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x ∈ Ω ⊂ ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A = Lφ,E, B = Lψ,E, giving some optimal (or rather sharp) relations between ...
Evgeniy Pustylnik, Lech Maligranda
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Domains of pseudo‐differential operators: a case for the Triebel‐Lizorkin spaces
Journal of Function Spaces, Volume 3, Issue 3, Page 263-286, 2005., 2005 The main result is that every pseudo‐differential operator of type 1, 1 and order d is continuous from the Triebel‐Lizorkin space Fp,1d to Lp, 1 ≤ p≺∞, and that this is optimal within the Besov and Triebel‐Lizorkin scales. The proof also leads to the known continuity for s≻d, while for all real s the sufficiency of Hörmander′s condition on the twisted ...
Jon Johnsen, Victor Burenkov
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Box dimension, oscillation and smoothness in function spaces
Journal of Function Spaces, Volume 3, Issue 3, Page 287-320, 2005., 2005 The aim of this paper is twofold. First we relate upper and lower box dimensions with oscillation spaces, and we develop embeddings or inclusions between oscillation spaces and Besov spaces. Secondly, given a point in the (1p, s)‐plane we determine maximal and minimal values for the upper box dimension (also the maximal value for lower box dimension ...
Abel Carvalho, Hans Triebel
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Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces
Open Mathematics, 2017 In Hörmander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions.
Los Valerii, Murach Aleksandr
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Hardy–Adams Inequalities on ℍ2 × ℝn-2
Advanced Nonlinear Studies, 2021 Let ℍ2{\mathbb{H}^{2}} be the hyperbolic space of dimension 2. Denote by Mn=ℍ2×ℝn-2{M^{n}=\mathbb{H}^{2}\times\mathbb{R}^{n-2}} the product manifold of ℍ2{\mathbb{H}^{2}} and ℝn-2(n≥3){\mathbb{R}^{n-2}(n\geq 3)}.
Ma Xing, Wang Xumin, Yang Qiaohua
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A sharpness result for powers of Besov functions
Journal of Function Spaces, Volume 2, Issue 3, Page 267-277, 2004., 2004 A recent result of Kateb asserts that f∈Bp,qs(ℝn) implies |f|μ∈Bp,qs(ℝn) as soon as the following three conditions hold: (1) 0≺s≺μ + (1/p), (2) f is bounded, (3) μ≻1. By means of counterexamples, we prove that those conditions are optimal.
Gérard Bourdaud, Jürgen Appell
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International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 37, Page 1973-1996, 2004., 2004 Simplified regularization using finite‐dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill‐posed operator equations. The derived error estimates using an a priori and a posteriori choice of parameters in relation to the noise level are shown to be of optimal order with ...
Santhosh George, M. Thamban Nair
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Limiting Sobolev inequalities and the 1-biharmonic operator
Advances in Nonlinear Analysis, 2014 In this article we present recent results on optimal embeddings, and associated PDEs, of the space of functions whose distributional Laplacian belongs to L1.
Parini Enea +2 more
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