Abstract
A new collection of Riesz sets for \(\mathbb{R}^n\) and \(\mathbb{Z}^n\) is exhibited. The results are new even in the one-dimensional case. The asymptotic estimate of Fourier multipliers on finite measures in the space \(H^{1,\infty }\) used in the proof is interesting in itself. Bibliography: 3 titles.
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REFERENCES
V. P. Havin and B. Jürike, The Uncertainty Principle in Harmonic Analysis, Springer-Verlag (1994).
M. M. Roginskaya, “Asymptotic lower estimate for multidimensional Calderon-Zygmund operators on singular measures,” Algebra Analiz, 9 (1997).
R. G. M. Brummelhuis, “A microlocal F. and M. Riesz theorem with applications,” Revista Mathemάtica Iberoamericana, 5, No. 1 (1989).
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Roginskaya, M.M. Two Multidimensional Analogs of the F. and M.~Riesz Theorem. Journal of Mathematical Sciences 107, 4083–4091 (2001). https://doi.org/10.1023/A:1012496818444
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DOI: https://doi.org/10.1023/A:1012496818444