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42e30 (secondary)

Journal of the London Mathematical Society (1)

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CALDERÓN–ZYGMUND OPERATORS ON MIXED LEBESGUE SPACES AND APPLICATIONS TO NULL FORMS
ATANAS STEFANOV, RODOLFO H. TORRES
Journal:

Journal of the London Mathematical Society / Volume 70 / Issue 2 / October 2004

Published online by Cambridge University Press:

01 October 2004, pp. 447-462

Print publication:

October 2004
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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.