441 research outputs found

    On relatively compact sets in quasi-Banach function spaces

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    This paper is devoted to the study of the relatively compact sets in Quasi-Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness criteria for function spaces with any weight without any assumption.Comment: To appear in Proc. Amer. Math. So

    Unimodular multipliers on α\alpha-modulation spaces: A revisit with new method under weaker conditions

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    By a new method derived from Nicola--Primo--Tabacco[24], we study the boundedness on α\alpha-modulation spaces of unimodular multipliers with symbol eiμ(ξ)e^{i\mu(\xi)}. Comparing with the previous results, the boundedness result is established for a larger family of unimodular multipliers under weaker assumptions

    Hausdorff operators on modulation and Wiener amalgam spaces

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    We give the sharp conditions for boundedness of Hausdorff operators on certain modulation and Wiener amalgam spaces.Comment: To appear in "Annals of Functional Analysis

    The Public and Its Problem: Dewey, Habermas, and Levinas

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    The question of who defines the public in public education in a democratic society is a tricky one. It is tricky because the answer appears deceivingly obvious, but it is also deeply difficult. In a democratic society, the decisions about public education seem, by default, to be made by all people: concerned citizens, parents, or those who live within the borders of the district/state/nation, and who, presumably, share certain common values, interests, or purposes related to the future of the children and the place

    A New Splitting Method for Time-dependent Convection-dominated Diffusion Problems

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    We present a new splitting method for time-dependent convection-dominated diffusion problems. The original convection diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a convection problem and a diffusion problem are solved successively. The scheme has the following nice features: the convection subproblem is solved explicitly and a multistep technique is introduced to essentially enlarge the stability region so that the resulting scheme behaves like an unconditionally stable scheme; the diffusion subproblem is always self-adjoint and coercive so that it can be solved efficiently using many existing optimal preconditioned iterative solvers. The scheme is then extended for Navier-Stokes equations, where the nonlinear convection is resolved by a linear explicit multistep scheme at the convection step, and only a generalized Stokes problem is needed to solve at the diffusion step with the resulting stiffness matrix being invariant in the time marching process. The new schemes are all free from tuning some stabilization parameters for the convection-dominated diffusion problems. Numerical simulations are presented to demonstrate the stability, convergence and performance of the single-step and multistep variants of the new scheme.Comment: 24 pages, 6 gigure

    Full Characterization of embedding relations between alpha modulation spaces

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    In this paper, we consider the embedding relations between any two α\alpha% -modulation spaces. Based on an observation that the α\alpha-modulation space with smaller α\alpha can be regarded as a corresponding α\alpha% -modulation space with larger α\alpha, we give a complete characterization of the Fourier multipliers between α\alpha-modulation spaces with different α\alpha. Then we establish a full version of optimal embedding relations between α\alpha-modulation spaces. As an application, we determine that the bounded operators commuting with translations between α\alpha-modulation spaces are of convolution type

    Sharp estimates of unimodular Fourier multipliers on Wiener amalgam spaces

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    We study the boundedness on the Wiener amalgam spaces Wsp,qW^{p,q}_s of Fourier multipliers with symbols of the type eiμ(ξ)e^{i\mu(\xi)}, for some real-valued functions μ(ξ)\mu(\xi) whose prototype is ξβ|\xi|^{\beta} with β(0,2]\beta\in (0,2]. Under some suitable assumptions on μ\mu, we give the characterization of Wsp,qWp,qW^{p,q}_s\rightarrow W^{p,q} boundedness of eiμ(D)e^{i\mu(D)}, for arbitrary pairs of 0<p,q0< p,q\leq \infty. Our results are an essential improvement of the previous known results, for both sides of sufficiency and necessity, even for the special case μ(ξ)=ξβ\mu(\xi)=|\xi|^{\beta} with 1<β<21<\beta<2

    Limiting weak-type behaviors for factional maximal operators and fractional integrals with rough kernel

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    By a reduction method, the limiting weak-type behaviors of factional maximal operators and fractional integrals are established without any smoothness assumption on the kernel, which essentially improve and extend previous results. As a byproduct, we characterize the boundedness of several operators by the membership of their kernel in Lebesgue space on sphere.Comment: Some typos are correcte

    Matrix dilation and Hausdorff operators on modulation spaces

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    In this paper, we establish the asymptotic estimates for the norms of the matrix dilation operators on modulation spaces. As an application, we study the boundedness on modulation spaces of Hausdorff operators. The definition of Hausdorff operators are also revisited for fitting our study

    The unboundedness of Hausdorff operators on Quasi-Banach spaces

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    In this note, we show that the Hausdorff operator HΦH_{\Phi} is unbounded on a large family of Quasi-Banach spaces, unless HΦH_{\Phi} is a zero operator
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