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Besov spaces. --- Besov, Espaces de.

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Boundary value problems. --- Elliptic operators. --- Besov spaces --- Problèmes aux limites --- Opérateurs elliptiques --- Espaces de Besov --- Boundary value problems --- Elliptic operators --- Problèmes aux limites --- Opérateurs elliptiques

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Mathematical analysis --- Functional analysis --- 51 --- Mathematics --- Differential equations, Partial. --- Initial value problems. --- Besov spaces. --- 51 Mathematics --- Besov spaces --- Besov, Espaces de --- 51 Wiskunde. Mathematiek --- Wiskunde. Mathematiek --- Equations aux derivees partielles --- Differences finies --- Equations aux derivees partielles hyperboliques --- Approximation des solutions --- Problemes de valeurs initiales

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This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis. Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, Lp spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.

Fourier analysis. --- Functional analysis. --- Mathematics. --- Fourier Analysis. --- Functional Analysis. --- Real Functions. --- Math --- Science --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Fourier --- Mathematical analysis --- Besov spaces. --- Functions of real variables. --- Real variables --- Functions of complex variables

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Differential equations, Partial --- Navier-Stokes equations --- Fluid mechanics --- Compressibility --- Besov spaces --- Equations aux dérivées partielles --- Navier-Stokes, Equations de --- Fluides, Mécanique des --- Compressibilité --- Besov, Espaces de --- Équations aux dérivées partielles. --- Navier-Stokes, Équations de. --- Fluides, Mécanique des. --- Compressibilité. --- Besov, Espaces de. --- Mécanique des fluides.