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Calderón–Zygmund Operators on Mixed Lebesgue Spaces and Applications to Null Forms
Author(s) -
Stefanov Atanas,
Torres Rodolfo H.
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005502
Subject(s) - mathematics , lp space , pure mathematics , lebesgue integration , sobolev space , standard probability space , lebesgue–stieltjes integration , lebesgue's number lemma , space (punctuation) , bilinear interpolation
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 ,υ) =∂ i u∂ j υ − ∂ j u∂ i υ, Q 0 ( u ,υ)= u t υ t −∇ x u· ∇ x υ on various space–time mixed Sobolev–Lebesgue spaces is shown.