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 areas 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.In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions.

This book gives a unified approach to the theory concerning a new matrix version of classical harmonic analysis. Most results in the book have their analogues as classical or newer results in harmonic analysis. It can be used as a source for further research in many areas related to infinite matrices. In particular, it could be a perfect starting point for students looking for new directions to write their PhD thesis as well as for experienced researchers in analysis looking for new problems with great potential to be very useful both in pure and applied mathematics where classical analysis has been used, for example, in signal processing and image analysis.

Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

This book project was initiated at "The Tribute Workshop in Honour of Gunnar Sparr" and the follow-up workshop "Inequalities, Interpolation, Non-commutative, Analysis, Non-commutative Geometry and Applications INANGA08," held at the Centre for Mathematical Sciences, Lund University in May and November of 2008.

The resulting book is dedicated in celebration of Gunnar Sparr's sixty-fifth anniversary and more than forty years of exceptional service to mathematics and its applications in engineering and technology, mathematics and engineering education, as well as interdisciplinary, industrial and international cooperation.
This book presents new advances in several areas of mathematics and engineering mathematics including applications in modern technology, engineering and life sciences. Thirteen high-quality chapters put forward many new methods and results, reviews of up to date research and open directions and problems for future research.
A special chapter by Gunnar Sparr and Georg Lindgren contains a historical account and important aspects of engineering mathematics
research and education, and the implementation of the highly successful education programme in Engineering Mathematics at Lund Institute of Technology, where not only the mathematical sciences have played a role.
This book will serve as a source of inspiration for a broad spectrum of researchers and research students."

This book project was initiated at "The Tribute Workshop in Honour of Gunnar Sparr" and the follow-up workshop "Inequalities, Interpolation, Non-commutative, Analysis, Non-commutative Geometry and Applications INANGA08," held at the Centre for Mathematical Sciences, Lund University in May and November of 2008.

The resulting book is dedicated in celebration of Gunnar Sparr's sixty-fifth anniversary and more than forty years of exceptional service to mathematics and its applications in engineering and technology, mathematics and engineering education, as well as interdisciplinary, industrial and international cooperation.
This book presents new advances in several areas of mathematics and engineering mathematics including applications in modern technology, engineering and life sciences. Thirteen high-quality chapters put forward many new methods and results, reviews of up to date research and open directions and problems for future research.
A special chapter by Gunnar Sparr and Georg Lindgren contains a historical account and important aspects of engineering mathematics
research and education, and the implementation of the highly successful education programme in Engineering Mathematics at Lund Institute of Technology, where not only the mathematical sciences have played a role.
This book will serve as a source of inspiration for a broad spectrum of researchers and research students."

Convex functions play an important role in almost all branches of mathematics as well as other areas of science and engineering. This book is a thorough introduction to contemporary convex function theory addressed to all people whose research or teaching interests intersect with the field of convexity. It covers a large variety of subjects, from the one real variable case (with all its mathematical gems) to some of the most advanced topics such as Choquet's theory, the Pr kopa-Leindler type inequalities and their ramifications, as well as the variational approach of partial differential equations and convex programming. Many results are new and the whole book reflects the authors own experience, both in teaching and research. The book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering and it can also be used for graduate courses.

This volume contains 16 refereed research articles on function spaces, interpolation theory and related fields. Topics covered: theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, special functions, homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets. The book will be of interest to both researchers and graduate students working in interpolation theory, function spaces and operators, partial differential equations and analysis on bounded symmetric domains.

This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.

This book is highly recommended for students in high schools and those studying privately for other entrance examination to the universities. It is suitable as a preparatory course book for those who wish to engage in self-study through distance learning programmes in the universities and other tertiary educational institutions.The book begins with an introductory work on arithmetic that includes the number line, fractions, approximations, etc. This is followed by chapters which cover extensively the syllables of major examinations such as the GCE O'Level and the WASSE examinations.

Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

The book may be considered as a systematic and detailed analysis of a wide class of integral transforms with product kernels from the two-weighted boundedness point of view. The considered product kernels cover that case when factors of kernels have essential (less than one) singularities. The book intends to make a breakthrough in two directions: to cover multidimensional potentials, Hilbert transforms, strong maximal functions and at the same time, to present solutions of two-weighted problems for them which are much more complicated than one-weighted ones. In the given monograph two-weighted boundedness criteria for multiple Hardy transforms is reflected in the case when the two-dimensional weight on the right-hand side of an appropriate inequality is a product of two weight functions of single variable. In this case we present simpler and transparent criteria than those of E Sawyer for general weights. Moreover, we prove some new multidimensional Hardy{ type inequalities with general kernels. Weighted integral in-equalities for monotonic functions of several variables are also discussed. The main subjects of this book can be useful for applications both within various areas of the mathematical sciences (e.g. Fourier and Harmonic analysis, Fractional Calculus, BVP of PDE in Mathematical Physics, Stochastic Processes, Error Estimates in Numerical Analysis, etc.) as well as directly in some applied sciences.