Weighted inequalities, limiting real interpolation and function spaces
| Thesis title in Czech: | Váhové nerovnosti, limitní reálná interpolace a prostory funkcí |
|---|---|
| Thesis title in English: | Weighted inequalities, limiting real interpolation and function spaces |
| Key words: | Banachovy prostory funkcí|Teorie reálné interpolace|Váhové nerovnosti|pomalu se měnící funkce|K- a J-prostory|Kompaktnost|Míra nekompaktnosti|Dualita |
| English key words: | Banach function spaces|Theory of real interpolation|Weighted inequalitis|Slowly-varying functions|K- and J- spaces|Compactness|Measure of non-compactness|Duality |
| Academic year of topic announcement: | 2018/2019 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| Department: | Department of Mathematical Analysis (32-KMA) |
| Supervisor: | doc. RNDr. Bohumír Opic, DrSc. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 27.09.2018 |
| Date of assignment: | 27.09.2018 |
| Confirmed by Study dept. on: | 29.10.2018 |
| Date and time of defence: | 18.03.2024 10:40 |
| Date of electronic submission: | 17.02.2024 |
| Date of submission of printed version: | 17.02.2024 |
| Date of proceeded defence: | 18.03.2024 |
| Opponents: | Lars-Erik Persson |
| doc. RNDr. Aleš Nekvinda, CSc. | |
| Guidelines |
| Weighted inequalities play an important role in many areas of mathematical analysis (e.g., in the theory of function spaces, approximation theory and interpolation theory). The aim of the work is get acquainted with the actual state of these disciplines and to derive new results. |
| References |
| [1] B. Opic and A. Kufner, Hardy-type inequalities. Pitman Research Notes in Mathematics Series 219, Longman Scientific & Technical, Harlow, 1990.
[2] A. Kufner and L.-E. Persson, Weighted inequalities of Hardy type. World Scientific Publishing Co., New Jersey, 2003. [3] W. D. Evans, A. Gogatishvili and B. Opic, Weighted inequalities involving $\rho$�-quasiconcave operators. To appear in World Scientific Publishing Co. [4] J. Bergh and J. Löfström, Interpolation Spaces. Springer, Berlin, 1976. [5] C. Bennett and R. Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol. 129. Academic, New York, 1988. [6] Yu.A. Brudnyi and N.Ya. Kruglyak, Interpolation functors and interpolation spaces, North Holland, Amsterdam,1991. [7] A. Kufner, O. John and S. Fučík, Function spaces, Noordhoff, Leyden, Academia, Praha, 1977. [8] L. Pick, A. Kufner, O. John and S. Fučík, Function spaces, vol. 1, De Gruyter, Berlin/Boston, 2013. [9] R. A. Adams and J. J. F. Fournier, Sobolev spaces, Pure and Applied Mathematics 140, Academic Press, Amsterdam, 2003. [10] A. Gogatishvili and V. D. Stepanov, Reduction theorems for operators on the cones of monotone functions, J. Math. Anal. Appl. 405, no. 1, 156--172 (2013). [11] A. Gogatishvili, B. Opic and W. Trebels, Limiting reiteration for real interpolation with slowly varying functions, Math. Nachr. 278, no. 1-2, 86--107 (2005). |