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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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On Extended Hardy-hilbert Integral Inequalities And Applications (Hardcover)
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On Extended Hardy-hilbert Integral Inequalities And Applications (Hardcover)
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Hilbert-type inequalities, including Hilbert's inequalities proved
in 1908, Hardy-Hilbert-type inequalities proved in 1934, and
Yang-Hilbert-type inequalities first proved around 1998, play an
important role in analysis and its applications. These inequalities
are mainly divided in three classes: integral, discrete and
half-discrete. During the last twenty years, there have been many
research advances on Hilbert-type inequalities, and especially on
Yang-Hilbert-type inequalities.In the present monograph, applying
weight functions, the idea of parametrization as well as techniques
of real analysis and functional analysis, we prove some new
Hilbert-type integral inequalities as well as their reverses with
parameters. These inequalities constitute extensions of the
well-known Hardy-Hilbert integral inequality. The equivalent forms
and some equivalent statements of the best possible constant
factors associated with several parameters are considered.
Furthermore, we also obtain the operator expressions with the norm
and some particular inequalities involving the Riemann-zeta
function and the Hurwitz-zeta function. In the form of
applications, by means of the beta function and the gamma function,
we use the extended Hardy-Hilbert integral inequalities to consider
several Hilbert-type integral inequalities involving derivative
functions and upper limit functions. In the last chapter, we
consider the case of Hardy-type integral inequalities. The lemmas
and theorems within provide an extensive account of these kinds of
integral inequalities and operators.Efforts have been made for this
monograph hopefully to be useful, especially to graduate students
of mathematics, physics and engineering, as well as researchers in
these domains.
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