Abstract
We study the Littlewood-Paley theory for multiple Fourier series with arbitrary period lattice. It is shown that the constants in the Littlewood-Paley inequality can be chosen to be independent of the mutual arrangement of the period lattice and the set of dyadic parallelepipeds. Bibliography: 6 titles.
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References
M. M. Skriganov, “Uniform distributions and geometry of numbers,” Preprint LOMI P-6-91, Leningrad (1981).
M. M. Skriganov, “Constructions of uniform distributions in terms of geometry of numbers,”Algebra Analiz,6, No. 3, 200–230 (1994).
E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, New Jersey (1970).
S. M. Nikolskii,Approximation of Functions of Several Variables and Imbedding Theorems, Springer-Verlag, New York-Heidelberg (1975).
E. M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, New Jersey (1971).
M. M. Skriganov, “Geometric and arithmetic methods in the spectral theory of multi-dimensional periodic operators,”Tr. Mat. Inst. Akad. Nauk SSSR,171 (1984).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 155–169.
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Skriganov, M.M. The Littlewood-Paley theory for multiple Fourier series. J Math Sci 89, 1021–1030 (1998). https://doi.org/10.1007/BF02358539
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DOI: https://doi.org/10.1007/BF02358539