Spectral Theory, Function Spaces and Inequalities

1. Front Matter

   Pages i-xii

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2. Generalised Meissner Equations with an Eigenvalue-inducing Interface

   • B. M. Brown, M. S. P. Eastham

   Pages 1-20

3. On the HELP Inequality for Hill Operators on Trees

   • B. M. Brown, K. M. Schmidt

   Pages 21-36

4. Measure of Non-compactness of Operators Interpolated by Limiting Real Methods

   • Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez

   Pages 37-54

5. A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality

   • Rupert L. Frank, Elliott H. Lieb

   Pages 55-67

6. Dichotomy in Muckenhoupt Weighted Function Space: A Fractal Example

   • Dorothee D. Haroske

   Pages 69-89

7. Lavrentiev’s Theorem and Error Estimation in Elliptic Inverse Problems

   • Ian Knowles, Mary A. LaRussa

   Pages 91-103

8. Two-weighted Norm Inequalities for the Double Hardy Transforms and Strong Fractional Maximal Functions in Variable Exponent Lebesgue Space

   • Vakhtang Kokilashvili, Alexander Meskhi

   Pages 105-124

9. Modular Eigenvalues of the Dirichlet p(·)-Laplacian and Their Stability

   • Jan Lang, Osvaldo Méndez

   Pages 125-137

10. Spectral Properties of Some Degenerate Elliptic Differential Operators

    • Roger T. Lewis

    Pages 139-156

11. Continuous and Compact Embeddings of Bessel-Potential-Type Spaces

    • Bohumír Opic

    Pages 157-196

12. A Sequence of Zero Modes of Weyl–Dirac Operators and an Associated Sequence of Solvable Polynomials

    • Yoshimi Saitō, Tomio Umeda

    Pages 197-209

13. A Szegő Limit Theorem for Operators with Discontinuous Symbols in Higher Dimensions: Widom’s Conjecture

    • Alexander V. Sobolev

    Pages 211-231

14. On a Supremum Operator

    • Vladimir D. Stepanov

    Pages 233-242

15. Entropy Numbers of Quadratic Forms and Their Applications to Spectral Theory

    • Hans Triebel

    Pages 243-262

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.

• Differential equations
• Function spaces
• Interpolation theory
• Operator theory

• School of Computer Science, Cardiff University, Cardiff, United Kingdom

  B. Malcolm Brown

• Dept. Mathematics, Ohio State University, Columbus, USA

  Jan Lang

• School of Mathematics, Statistics &, Actuarial Science, University of Kent, Canterbury, Kent, United Kingdom

  Ian G. Wood

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