Fourier Analysis

Duoandikoetxea, Javier

doi:10.1090/gsm/029

Cited by 402 publications

(341 citation statements)

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“…However, even this number of derivatives is too big from the viewpoint of the linear case. Exploiting the idea of the proof of the Hörmander multiplier theorem in [5], Tomita [15] proved the following result in the m-linear case:…”

Section: Introductionmentioning

confidence: 99%

The Hörmander multiplier theorem for multilinear operators

Grafakos

2012

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Section: Introductionmentioning

confidence: 99%

The Hörmander multiplier theorem for multilinear operators

Grafakos

2012

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…This, together with the boundedness of on 2 (R ) (see [34]), tells us that is a generalized Calderón-Zygmund operator ( [33]). Thus, by applying Lemma 10, we see that is bounded froṁ, ,1 (R ) tȯ, ,1 (R ) with bound (‖∇ ‖ ∞ ( −1 ) +‖ ‖ ∞ ( −1 ) )‖∇ ‖ ∞ for 0 ≤ ≤ ∞, −1 < < , and 0 < < ∞.…”

Section: Lemma 12 Let ( ) Be a Homogeneous Of Degree − − 1 And Localmentioning

confidence: 93%

“…It is well known that is weak (1) (e.g., see [33]). Noticing that satisfying (18) with = 0, then we can obtain Lemma 10 by using Lemma 8.…”

Section: Preliminaries and Main Lemmasmentioning

confidence: 99%

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

Yang

Tao

2017

Journal of Function Spaces

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Let be the singular integral operator with variable kernel defined by ( ) = p.v. ∫ R (Ω( , − )/| − | ) ( )d and let (0 ≤ ≤ 1) be the fractional differentiation operator. Let * and ♯ be the adjoint of and the pseudoadjoint of , respectively. In this paper, the authors prove that − and ( * − ♯ ) are bounded, respectively, from Morrey-Herz spaceṡ, ,1 (R ) to the weak Morrey-Herz spaceṡ, ,1 (R ) by using the spherical harmonic decomposition. Furthermore, several norm inequalities for the product 1 2 and the pseudoproduct 1 ∘ 2 are also given.

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“…Interpolating between them (see [7,Theorem 2.4]) we obtain the following theorem. Proof of Theorem A.1follows at once from Theorem A.8, (A.8), (A.13), (A.15) and compactness of Ω.…”

Section: A12 the Pencil Operatormentioning

confidence: 99%

Solutions to the Navier–Stokes equations with mixed boundary conditions in two‐dimensional bounded domains

Beneš

Kučera

2015

Mathematische Nachrichten

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Abstract:In this paper we consider the system of the non-steady Navier-Stokes equations with mixed boundary conditions. We study the existence and uniqueness of a solution of this system. We define Banach spaces X and Y , respectively, to be the space of "possible" solutions of this problem and the space of its data. We define the operator N : X → Y and formulate our problem in terms of operator equations. Let u ∈ X and G P u : X → Y be the Frechet derivative of N at u. We prove that G P u is one-to-one and onto Y . Consequently, suppose that the system is solvable with some given data (the initial velocity and the right hand side). Then there exists a unique solution of this system for data which are small perturbations of the previous ones. Next result proved in the Appendix of this paper is W 2,2 -regularity of solutions of steady Stokes system with mixed boundary condition for sufficiently smooth data.

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Fourier Analysis

Cited by 402 publications

References 0 publications

The Hörmander multiplier theorem for multilinear operators

The Hörmander multiplier theorem for multilinear operators

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

Solutions to the Navier–Stokes equations with mixed boundary conditions in two‐dimensional bounded domains

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