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CALDERÓN–ZYGMUND OPERATORS ON MIXED LEBESGUE SPACES AND APPLICATIONS TO NULL FORMS

Published online by Cambridge University Press:  01 October 2004

ATANAS STEFANOV  and
RODOLFO H. TORRES
ATANAS STEFANOV
Affiliation:
Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, KS 66045–7523 [email protected]@math.ukans.edu
RODOLFO H. TORRES
Affiliation:
Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, KS 66045–7523 [email protected]@math.ukans.edu
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Abstract

The boundedness of Calderón–Zygmund operators is proved in the scale of the mixed Lebesgue spaces. As a consequence, the boundedness of the bilinear null forms $Q_{i j} (u,v) \,{=}\,\p_i u\p_j v \,{-}\, \p_j u\p_i v$, $Q_0(u,v)\,{=}\,u_t v_t \,{-}\,\nabla_x u\,{\cdot}\, \nabla_x v$ on various space–time mixed Sobolev–Lebesgue spaces is shown.

Keywords

42B20 (primary)42E30 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 447 - 462
Copyright
The London Mathematical Society 2004

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