Spectral Theory, Function Spaces and Inequalities New Techniques and Recent Trends

This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.

Preface.- David Edmunds' Mathematical Work.- Desmond Evans' mathematical work.- Generalised Meissner Equations with an Eigenvalue-inducing Interface.- On the HELP Inequality for Hill Operators on Trees.- Measure of Non-compactness of Operators Interpolated by Limiting Real Methods.- A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality.- Dichotomy in Muckenhoupt Weighted Function Space: A Fractal Example.- Lavrentiev's Theorem and Error Estimation in Elliptic Inverse Problems.- Two-weighted Norm Inequalities for the Double Hardy Transforms and Strong Fractional Maximal Functions in Variable Exponent Lebesgue Space.- Modular Eigenvalues of the Dirichlet p(.)-Laplacian and Their Stability.- Spectral Properties of Some Degenerate Elliptic Differential Operators.- Continuous and Compact Embeddings of Bessel-Potential-Type Spaces.- A Sequence of Zero Modes of Weyl–Dirac Operators and an Associated Sequence of Solvable Polynomials.- A Szegö Limit Theorem for Operators with Discontinuous Symbols in Higher Dimensions: Widom's Conjecture.- On a Supremum Operator.- Entropy Numbers of Quadratic Forms and Their Applications to Spectral Theory.