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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Theory of Besov Spaces (Hardcover, 1st ed. 2018)
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Theory of Besov Spaces (Hardcover, 1st ed. 2018)
Series: Developments in Mathematics, 56
Expected to ship within 10 - 15 working days
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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, L^p 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 Hoelder continuous spaces-are defined and discussed,
and it is shown that they are special cases of Besov spaces and
Triebel-Lizorkin spaces.
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