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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Hardy Inequalities on Homogeneous Groups - 100 Years of Hardy Inequalities (Hardcover, 1st ed. 2019)
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Hardy Inequalities on Homogeneous Groups - 100 Years of Hardy Inequalities (Hardcover, 1st ed. 2019)
Series: Progress in Mathematics, 327
Expected to ship within 12 - 17 working days
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This open access book provides an extensive treatment of Hardy
inequalities and closely related topics from the point of view of
Folland and Stein's homogeneous (Lie) groups. The place where Hardy
inequalities and homogeneous groups meet is a beautiful area of
mathematics with links to many other subjects. While describing the
general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg,
Sobolev, and other inequalities in the setting of general
homogeneous groups, the authors pay particular attention to the
special class of stratified groups. In this environment, the theory
of Hardy inequalities becomes intricately intertwined with the
properties of sub-Laplacians and subelliptic partial differential
equations. These topics constitute the core of this book and they
are complemented by additional, closely related topics such as
uncertainty principles, function spaces on homogeneous groups, the
potential theory for stratified groups, and the potential theory
for general Hoermander's sums of squares and their fundamental
solutions. This monograph is the winner of the 2018 Ferran Sunyer i
Balaguer Prize, a prestigious award for books of expository nature
presenting the latest developments in an active area of research in
mathematics. As can be attested as the winner of such an award, it
is a vital contribution to literature of analysis not only because
it presents a detailed account of the recent developments in the
field, but also because the book is accessible to anyone with a
basic level of understanding of analysis. Undergraduate and
graduate students as well as researchers from any field of
mathematical and physical sciences related to analysis involving
functional inequalities or analysis of homogeneous groups will find
the text beneficial to deepen their understanding.
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