Multipliers in the scale of periodic Bessel potential spaces with smoothness indices of different signs

2022/12/12 by A. A. Belyaev, Belyaev, Alexei A., Андрей Андреевич Шкаликов +1
Mathematics · #42B15 (Secondary) #42B35 (Primary) #46E35 #46F05 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2212.05681

openalex publication_date 2022/12/12 · openalex created_date 2022/12/26 · openalex updated_date 2026/07/28

Abstract

We prove a general type description result for the multipliers acting between two periodic Bessel potential spaces, defined on the n--dimensional torus, in a case when their smoothness indices are of different signs. This is done through the detailed examination of a periodic analogue of the linear operator J_s, which is employed in the definition of the scale of the Bessel potential space defined on the whole space ℝⁿ. Our method of defining this periodic analogue of J_s uses the results about an asymptotic behaviour of the generalized Fourier coefficients and existence of a natural homeomorphism between the spaces D'(\mathbbTⁿ) and S'_{2 ⋅ π}(ℝⁿ), where the latter consists of all 2 ⋅ π--periodic distributions from the dual Schwartz space S'(ℝⁿ).

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