The Hardy Inequality
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| Author | : Michael Ruzhansky |
| Publisher | : Springer |
| Total Pages | : 579 |
| Release | : 2019-07-02 |
| Genre | : Mathematics |
| ISBN | : 303002895X |
Download Hardy Inequalities on Homogeneous Groups Book in PDF, Epub and Kindle
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 Hörmander'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.
| Author | : Alexander A. Balinsky |
| Publisher | : Springer |
| Total Pages | : 277 |
| Release | : 2015-10-20 |
| Genre | : Mathematics |
| ISBN | : 3319228706 |
Download The Analysis and Geometry of Hardy's Inequality Book in PDF, Epub and Kindle
This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.
| Author | : Alois Kufner |
| Publisher | : |
| Total Pages | : 161 |
| Release | : 2007 |
| Genre | : |
| ISBN | : 9788086843155 |
Download The Hardy Inequality Book in PDF, Epub and Kindle
| Author | : B. Opic |
| Publisher | : |
| Total Pages | : 351 |
| Release | : 1990-01-01 |
| Genre | : |
| ISBN | : 9780608035987 |
Download Hardy-Type Inequalities Book in PDF, Epub and Kindle
| Author | : Dierk Schleicher |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 225 |
| Release | : 2011-05-19 |
| Genre | : Mathematics |
| ISBN | : 3642195334 |
Download An Invitation to Mathematics Book in PDF, Epub and Kindle
This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is about. We hope that it will also be of interest to teachers or more advanced mathematicians who would like to learn about exciting aspects of mathematics outside of their own work or specialization. Together with a team of young ``test readers'', editors and authors have taken great care, through a substantial ``active editing'' process, to make the contributions understandable by the intended readership.
| Author | : Karl-Goswin Grosse-Erdmann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 132 |
| Release | : 1998-01-19 |
| Genre | : Mathematics |
| ISBN | : 9783540639022 |
Download The Blocking Technique, Weighted Mean Operators and Hardy's Inequality Book in PDF, Epub and Kindle
This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis.
| Author | : Alois Kufner |
| Publisher | : World Scientific |
| Total Pages | : 380 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9789812381958 |
Download Weighted Inequalities of Hardy Type Book in PDF, Epub and Kindle
Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.
| Author | : Nikolai Kutev |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 158 |
| Release | : 2022-10-24 |
| Genre | : Mathematics |
| ISBN | : 3110980371 |
Download Hardy Inequalities and Applications Book in PDF, Epub and Kindle
This book derives new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. We focus on the optimality of Hardy constant and on its attainability. Applications include: results about existence\nonexistence and controllability for parabolic equations with double singular potentials; estimates from below of the fi rst eigenvalue of p-Laplacian with Dirichlet boundary conditions.
| Author | : Michail Borsuk |
| Publisher | : Elsevier |
| Total Pages | : 538 |
| Release | : 2006-01-12 |
| Genre | : Mathematics |
| ISBN | : 0080461735 |
Download Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains Book in PDF, Epub and Kindle
The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. Key features: * New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
| Author | : Alois Kufner |
| Publisher | : |
| Total Pages | : 16 |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
Download The Hardy Inequality Book in PDF, Epub and Kindle
