Q Spaces of Several Real Variables
نویسندگان
چکیده
For 2 (?1; 1), let Q (R n) be the space of all measurable functions with supp`(I)] 2?n Z I Z I jf(x) ? f(y)j 2 jx ? yj n+2 dx dy < 1; where the supremum is taken over all cubes I with the edge length`(I) and the edges parellel to the coordinate axes in R n. If 2 (?1; 0), then Q (R n) = BMO(R n), and if 2 1; 1), then Q (R n) = fconstantsg. In the present paper, we discuss the case 2 0; 1). These spaces are new subspaces of BMO(R n) containing some special Besov spaces. We characterize functions in Q (R n) by means of the Poisson extension, p-Carleson measures, mean oscillation and wavelet coeecients, and give a dyadic counterpart. Finally, we pose some open problems.
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