During this paintings, Han and Sawyer expand Littlewood-Paley conception, Besov areas, and Triebel-Lizorkin areas to the final environment of an area of homogeneous sort. For this goal, they determine an appropriate analogue of the Calderon reproducing formulation and use it to increase classical effects on atomic decomposition, interpolation, and T1 and Tb theorems. a few new leads to the classical surroundings also are received: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin areas with basically part the standard smoothness and cancellation stipulations at the approximate identification.

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