Spherical summation : a problem of E.M. Stein
Antonio Cordoba, B. Lopez-Melero (1981)
Annales de l'institut Fourier
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Writing . E. Stein conjectured for , and . We prove this conjecture. We prove also a.e. We only assume .
Antonio Cordoba, B. Lopez-Melero (1981)
Annales de l'institut Fourier
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Writing . E. Stein conjectured for , and . We prove this conjecture. We prove also a.e. We only assume .
Jean Bourgain (1985)
Annales de l'institut Fourier
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Assume a finite set of functions in , the space of bounded analytic functions on the open unit disc. We give a sufficient condition on a function in to belong to the norm-closure of the ideal generated by , namely the property for some function : satisfying The main feature in the proof is an improvement in the contour-construction appearing in L. Carleson’s solution of the corona-problem. It is also shown that the property ...
H. Hueber, M. Sieveking (1982)
Annales de l'institut Fourier
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Let , be elliptic operators with Hölder continuous coefficients on a bounded domain of class . There is a constant depending only on the Hölder norms of the coefficients of and its constant of ellipticity such that where (resp. ) are the Green functions of (resp. ) on .
Antonio Cordoba (1982)
Annales de l'institut Fourier
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In this paper we continue the study of the Fourier transform on , , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of , where is the number of equal angles considered in . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of , ,...
Hugh L. Montgomery (1976)
Annales de l'institut Fourier
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Let , where the are the numbers rearranged so that . Then for any convex increasing , . The special case , , gives an equivalent of Littlewood.