Paul, Debasish (2025) Lp Boundedness of Spherical Maximal Function. Masters thesis, Indian Institute of Science Education and Research Kolkata.
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Text (MS dissertation of Debasish Paul (23MP033))
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Abstract
The spherical maximal function is a central object in harmonic analysis that captures the behavior of averages of functions over spheres. It plays a crucial role in understanding pointwise convergence problems, particularly those arising in ergodic theory and partial differential equations. This paper investigates the boundedness properties of the spherical maximal operator. The analysis leverages tools from Fourier analysis, Littlewood–Paley theory, and geometric measure theory. The process of showing boundedness of maximal operator (spherical) relies on weak and strong type bounds. An interpolation theorem does the rest job.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | Supervisor: Dr. Sayan Bagchi |
| Uncontrolled Keywords: | Bessel Functions; Fourier Transform; Harmonic Analysis; Maximal Functions; Schwartz Space; Stein’s Theorem |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Department of Mathematics and Statistics |
| Depositing User: | IISER Kolkata Librarian |
| Date Deposited: | 22 Oct 2026 07:16 |
| Last Modified: | 22 Oct 2026 07:23 |
| URI: | http://eprints.iiserkol.ac.in/id/eprint/2389 |
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