A remark on fractional integrals on modulation spaces
Sep 5, 2008 ... A remark on fractional integrals on modulation spaces. Mitsuru Sugimoto. ∗1 and Naohito Tomita. ∗∗2. 1 Graduate School of Mathematics, ...
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Modulation space estimates for the fractional integral operators
Jul 12, 2011 ... modulation spaces modulation Hardy spaces fractional integral operator ... Tomita N. A remark on fractional integrals on modulation spaces.
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The inclusion relation between Sobolev and modulation spaces
The inclusion relations between the Lp-Sobolev spaces and the modulation spaces is determined ... A remark on fractional integrals on modulation spaces. Math ...
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Modulation Spaces, Wiener Amalgam Spaces - Western CEDAR
Bényi, Árpád and Oh, Tadahiro, "Modulation Spaces, Wiener Amalgam Spaces, .... Some immediate applications of Brownian motion regularity to stochastic integrals and ... stochastic calculus with respect to (fractional) Brownian motion and its .... Proposition 2.1 and Remark 4.2 in [42] show that the localized versions , say in ...
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Critical exponent for evolution equation in Modulation space
Nov 12, 2014 ... for certain evolution equations in modulation spaces. We define an index σ(s, q), and use it to determine the critical exponent of the fractional heat equation as an .... Remark 1. In this theorem ..... Consider the integral equation.
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Modulation spaces, Wiener amalgam spaces, and Brownian motions
modulation spaces and Wiener amalgam spaces are nowadays present in ... Some immediate applications of Brownian motion regularity to stochastic integrals and ... stochastic calculus with respect to (fractional) Brownian motion and its .... Proposition 2.1 and Remark 4.2 in [42] show that the localized versions , say in ...
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Smooth pointwise multipliers of modulation spaces
Key Words: Pointwise multipliers, Modulation spaces, Amalgam spaces, Bessel potential spaces. ... We remark that we will not consider the theory of Fourier multipliers of ..... With applications to differential and integral operators, Grundlehren der ... [15] R. S. Strichartz, Multipliers on fractional Sobolev spaces, J. Math. and.
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MULTILINEAR ESTIMATES ON FREQUENCY-UNIFORM
spaces for the bilinear Hilbert transform, bilinear fractional integral, the pointwise ... of the multilinear operator T(f1, ..., fm) on the modulation spaces as follows. .... Remark. Theorem 2 also holds if we replace the condition μi ∈ HL(Rn), L > n(. 1.
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REMARKS ON THE CAUCHY PROBLEM FOR THE ONE - Hal
In this paper, we consider actually the corresponding integral equation which is ... of results for the one-dimensional quadratic fractional heat equation (1.1). Indeed we will ... well-posedness in the Sobolev space 1 Hs(R), s ≥ 1/2 − 2α, unless α = 1/2. On the ...... We need to introduce the rescaled modulation spaces (M2,1)N.
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Fractional Operators, Dirichlet Averages, and Splines
erators defined on Lizorkin spaces is presented and some of their main properties exhibited. ..... and using Remark 2, we can write the definitions of the fractional integral and ..... tional modulation and phase factor in the frequency domain:.
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ABSTRACTS OF TALKS
Aug 14, 2015 ... We extended the known result that symbols from modulation spaces M ... [1] L. Caso, R. D'Ambrosio, and S. Monsurr`o, Some remarks on spaces of Morrey type, ... and the fractional integral operator on Morrey spaces.
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ESTIMATES FOR DAMPED FRACTIONAL WAVE EQUATIONS AND
Jun 16, 2015 ... Damped fractional wave equation; Lp-estimate; Strichartz estimate. c©2015 ... [1], we may also estimate the norm u(t, x)Lq (R+,Lp(Rn) by taking an integral of ..... By Young's inequality and Remark 3.3, we obtain ..... [21] C. Zhang; Strichartz estimates in the frame of modulation spaces, Nonlinear Analysis 78.
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Phase space analysis of semilinear parabolic equations
Aug 8, 2013 ... namely the modulation spaces, assuming a nonlinearity of analytic type. As another .... do not possess any fractional derivative in L2 loc. ... second order symbols b in (3); see the counterexamples in Remarks 5.1, 5.2 below. ... rough symbols, and [9, 14] for similar results for Fourier integral operators). Basi-.
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arXiv:1506.05827v2 [math.CA] 11 Apr 2016 - arXiv.org
UMD spaces, multilinear multipliers, multi-parameter singular integrals, outer ... [ Fractional Leibniz rules] For any α,β > 0, and functions fi : x × y → , ... amenable to treat modulation-invariant operators, in a similar fashion to Section 5 of [9]. ..... We also remark that our methods do not involve dyadic representation theorems of ...
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On persistence properties in fractional weighted spaces - American
Jun 3, 2015 ... dispersive equations in fractional weighted Sobolev spaces .... Remark. The identities (1.8)–(1.9) can be seen as an extension of (1.6) for ...
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MULTILINEAR SINGULAR INTEGRAL OPERATORS WITH
Abstract. Some recent results for bilinear or multilinear singular integrals ..... is the generalized Leibniz rule for fractional derivatives of the product of two func- ... ferential operators and modulation spaces see the works of Bényi, Gröchenig, Heil, ..... [30] G. Diestel, Some remarks on bilinear Littlewood-Paley theory, J. Math.
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SURGERY OF SPLINE-TYPE AND MOLECULAR FRAMES
Aug 31, 2009 ... spaces as models for the range of some integral transforms, we obtain some ... modulation spaces into spline-type spaces - considered in the ..... Remark 1. ..... An example to keep in mind are fractional Sobolev spaces Lq s.
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Asymptotic expansions of the error for hyper-singular integrals with
Keywords: hyper-singular integral; Euler-Maclaurin expansions; quadrature formulas ... on modulation spaces. ...... method in a different way just like in our remark. .... Calculate the hyper-singular integral with the fractional order singularity.
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Calderon-Zygmund theory - UCLA Department of Mathematics
In this set of notes we begin the theory of singular integral operators - operators which are almost ... (This is in contrast to, say, fractional integral .... be bounded on more normed spaces than just L2(R); in particular, it might be bounded .... Proof We remark that we could use the translation and scaling symmetries of. CZOs to ...
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New Trends in Harmonic and Complex Analysis - Jacobs University
Jun 29, 2010 ... Beurling-Helson theorem for modulation spaces ... Holomorphic self-maps of the disk intertwining two linear fractional maps. 11:00. Lev Aizenberg (Bar-Ilan). Remarks on the Bohr and Rogosinski phenomena for power series ... Representation of a function via the absolutely convergent Fourier integral.
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