Almost-everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an L-localisation principle.
Anthony Carbery, Fernando Soria (1988)
Revista Matemática Iberoamericana
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Anthony Carbery, Fernando Soria (1988)
Revista Matemática Iberoamericana
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Grant Welland (1972)
Studia Mathematica
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Soares De Souza, Geraldo (1989)
International Journal of Mathematics and Mathematical Sciences
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Avdispahić, M. (1986)
International Journal of Mathematics and Mathematical Sciences
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Wade, William R. (1982)
International Journal of Mathematics and Mathematical Sciences
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J. Marcinkiewicz, Antoni Zygmund (1939)
Fundamenta Mathematicae
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T. W. Körner (1981)
Colloquium Mathematicae
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Soares de Souza, Geraldo (1984)
International Journal of Mathematics and Mathematical Sciences
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Weisz, Ferenc (2005)
Annales Mathematicae et Informaticae
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Adam Osękowski (2014)
Open Mathematics
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We study sharp weak-type inequalities for a wide class of Fourier multipliers resulting from modulation of the jumps of Lévy processes. In particular, we obtain optimal estimates for second-order Riesz transforms, which lead to interesting a priori bounds for smooth functions on ℝd. The proofs rest on probabilistic methods: we deduce the above inequalities from the corresponding estimates for martingales. To obtain the lower bounds, we exploit the properties of laminates, important probability...
Fu Cheng Hsiang (1962-1964)
Compositio Mathematica
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