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https://olympias.lib.uoi.gr/jspui/handle/123456789/39140| Title: | The bases of intervals and rectangles in the two dimensional Euclidean space Οι βάσεις των διαστημάτων και των ορθογωνίων στον 2-διάστατο Ευκλείδειο χώρο |
| Institution and School/Department of submitter: | Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών |
| Keywords: | Differentiation,Bases,Rectangles,Euclidean space |
| URI: | https://olympias.lib.uoi.gr/jspui/handle/123456789/39140 |
| Table of contents: | 0 Preliminaries 1 1 The maximal function 7 1.1 Norm estimates for the maximal function . . . . . . . . . . . . . . . 7 1.2 The Hardy- Littlewood maximal theorem . . . . . . . . . . . . . . . 16 2 The basis B2 of intervals 19 2.1 Intervals of R2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Intervals of R3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3 The basis of rectangles B3 48 3.1 The Perron tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2 The needle problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3 The Besicovitch set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4 Differentiation properties of the basis of rectangles . . . . . . . . . . 69 4 The Decreasing Rearrangement 82 4.1 The distribution function . . . . . . . . . . . . . . . . . . . . . . . . 83 4.2 The decreasing rearrangement . . . . . . . . . . . . . . . . . . . . . . 86 4.3 Some results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5 Differentiability of multiple integrals 93 5.1 Introductory results . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.2 The case k=2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.3 The case of arbitary k . . . . . . . . . . . . . . . . . . . . . . . . . . 102 |
| Appears in Collections: | Διατριβές Μεταπτυχιακής Έρευνας (Masters) - ΜΑΘ |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| THESIS FINAL.pdf | 1.54 MB | Adobe PDF | View/Open |
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