Advances in Harmonic Analysis and Operator Theory

1. Front Matter

   Pages i-viii

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2. Stefan G. Samko – Mathematician, Teacher and Man

   • V. Kokilashvili

   Pages 1-48

3. The Role of S.G. Samko in the Establishing and Development of the Theory of Fractional Differential Equations and Related Integral Operators

   • Sergei V. Rogosin

   Pages 49-63

4. Energy Flow Above the Threshold of Tunnel Effect

   • F. Ali Mehmeti, R. Haller-Dintelmann, V. Régnier

   Pages 65-76

5. Some New Hardy-type Integral Inequalities on Cones of Monotone Functions

   • L. S. Arendarenko, R. Oinarov, L.-E. Persson

   Pages 77-89

6. On a Boundary Value Problem for a Class of Generalized Analytic Functions

   • P. Berglez, T. T. Luong

   Pages 91-99

7. The Factorization Problem: Some Known Results and Open Questions

   • Albrecht Böttcher, Ilya M. Spitkovsky

   Pages 101-122

8. A Class of Sub-elliptic Equations on the Heisenberg Group and Related Interpolation Inequalities

   • Jianqing Chen, Eugénio M. Rocha

   Pages 123-137

9. New Types of Solutions of Non-linear Fractional Differential Equations

   • Mark Edelman, Laura Anna Taieb

   Pages 139-155

10. Stability, Structural Stability and Numerical Methods for Fractional Boundary Value Problems

    • Neville J. Ford, M. Luísa Morgado

    Pages 157-173

11. On the Boundedness of the Fractional Maximal Operator, Riesz Potential and Their Commutators in Generalized Morrey Spaces

    • Vagif S. Guliyev, Parviz S. Shukurov

    Pages 175-199

12. Existence of Solutions of a Class of Nonlinear Singular Equations in Lorentz Spaces

    • L. Huang, K. Murillo, E. M. Rocha

    Pages 201-214

13. Growth of Schrödingerian Subharmonic Functions Admitting Certain Lower Bounds

    • Alexander I. Kheyfits

    Pages 215-231

14. The Riemann and Dirichlet Problems with Data from the Grand Lebesgue Spaces

    • V. Kokilashvili, V. Paatashvili

    Pages 233-251

15. Overview of Fractional h-difference Operators

    • Dorota Mozyrska, Ewa Girejko

    Pages 253-268

16. A Singularly Perturbed Dirichlet Problem for the Poisson Equation in a Periodically Perforated Domain. A Functional Analytic Approach

    • Paolo Musolino

    Pages 269-289

17. Fractional Variational Calculus of Variable Order

    • T. Odzijewicz, A. B. Malinowska, D. F. M. Torres

    Pages 291-301

18. Improving Bounds for Singular Operators via Sharp Reverse Höolder Inequality for \( A_\infty \)

    • Carmen Ortiz-Caraballo, Carlos Pérez, Ezequiel Rela

    Pages 303-321

19. Potential Type Operators on Weighted Variable Exponent Lebesgue Spaces

    • Vladimir Rabinovich

    Pages 323-347

20. A Note on Boundedness of Operators in Grand Grand Morrey Spaces

    • Humberto Rafeiro

    Pages 349-356

This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June‒July 2011.

• harmonic analysis
• operator theory
• potential theory

• , Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal

  Alexandre Almeida, Luís Castro

• Instituto Superior Tecnico, Depto. Matematica, Universidade Tecnica Lisboa, Lisboa, Portugal

  Frank-Olme Speck

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