Some consequences of Pisier’s approach to interpolation |
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Authors: | J Bourgain |
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Institution: | (1) Institut des Hautes Etudes Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, France;(2) University of Illinois, 61801 Urbana, IL, USA;(3) California Institute of Technology, 91125 Pasadena, CA, USA |
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Abstract: | A recent result of Pisier onK-functionals is exploited in the context of function spaces defined from singular integrals. The main consequences appear
forH
p
spaces on the complex ball (1≤p≤∞) and spaces of differentiable functions in several variables. It turns out that the complex variable arguments used in
P1] may in certain cases be substituted for real variable methods, which of course have a wider range of applicability. We
discuss interpolation of vector valued Hardy spaces on the ball and prove thatL
1(S)/H
1(B) satisfies Grothendieck’s theorem, similarly as in the disc case. |
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Keywords: | |
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