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Besov Spaces via Poisson Integrals

In: Real Analysis Methods for Markov Processes

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  • Kazuaki Taira

    (University of Tsukuba, The College of Mathematics)

Abstract

In this chapter we develop the theory of Besov spacesBesov space on the Euclidean space $$\textbf{R}^{n}$$ R n , paying particular attention to Poisson integralsPoisson integral. Besov spaces are function spaces defined in terms of the $$L^{p}$$ L p modulus of continuity, and enter naturally in connection with boundary value problems in the framework of Sobolev spaces of $$L^{p}$$ L p type. We prove a variety of equivalent norms for the Besov spaces on $$\textbf{R}^{n}$$ R n via Poisson integrals (Theorems 6.4, 6.7 and 6.8). The results discussed here are adapted from Taibleson [146] and Stein [137].

Suggested Citation

  • Kazuaki Taira, 2024. "Besov Spaces via Poisson Integrals," Springer Books, in: Real Analysis Methods for Markov Processes, chapter 0, pages 217-242, Springer.
    • Handle: RePEc:spr:sprchp:978-981-97-3659-1_6
    DOI: 10.1007/978-981-97-3659-1_6
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