Variational Carleson embeddings into the upper $3$-space
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- by Gennady Uraltsev;
- Trans. Amer. Math. Soc.
- DOI: https://doi.org/10.1090/tran/9401
- Published electronically: April 3, 2025
Abstract:
In this paper we formulate embedding maps into time-scale-frequency space related to the Carleson operator and its variational counterpart. We prove bounds for these embedding maps by iterating the outer measure theory of [Do and Thiele, Bull. Amer. Math. Soc. (N.S.) 52 (2015), pp. 249–296]. Introducing iterated outer $L^{p}$ spaces is a main novelty of this paper.References
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Bibliographic Information
- Gennady Uraltsev
- Affiliation: Department of Mathematical Sciences, 1 University of Arkansas, Fayetteville, Arkansas 72701
- MR Author ID: 1073181
- ORCID: 0000-0002-4781-3178
- Email: gennady.uraltsev@gmail.com
- Received by editor(s): March 27, 2017
- Received by editor(s) in revised form: December 27, 2022, December 27, 2022, March 17, 2023, June 23, 2024, and December 9, 2024
- Published electronically: April 3, 2025
- © Copyright 2025 by the authors
- Journal: Trans. Amer. Math. Soc.
- MSC (2020): Primary 42A20, 42B35; Secondary 42A45
- DOI: https://doi.org/10.1090/tran/9401