A Remark on the Boundedness of Calderón–Zygmund Operators in Nony–homogeneous Spaces

The Hardy Space H1 with Non-doubling Measures and Their Applications

“…• Theorem 8.3.4 was established by Fu et al in[27] for .X ; d; / WD .R D ; j j; / with satisfying the polynomial growth condition (0.0.1) and by Liu et al in[91] for a general metric measure spaces .X ; d; /. It is still unclear whether the conclusions of Theorem 8.3.4 and Corollary 8.3.5 hold true or not, if we replace the coefficient 1 C ı.B; S/ by its discrete counterpart Q ı .…”

Maximal multilinear Calderón-Zygmund operators with non-doubling measures

“…It is well-known that the doubling condition in the analysis of spaces of homogeneous type is a key assumption. In recent years, many research results indicated that the doubling condition is superuous for most of the classical CalderónZygmund theory; see, for example, [2,9,10,11,14,15,18]. We point out that the analysis on R d with non-doubling measures was proved to play a striking role in solving the long-standing open Painlevé's problem by Tolsa in [17]; see also [19] for more background of this.…”

Multilinear Calderón–Zygmund operators on the product of Lebesgue spaces with non-doubling measures

“…We recall that μ is said to satisfy the doubling condition if there exists some positive constant C such that μ(B(x, 2r)) Cμ(B(x, r)) for all x ∈ supp μ and r > 0. In recent years, a lot of papers focus on the study of function spaces with non-doubling measures and the boundedness of Calderón-Zygmund operators on these spaces and show that the doubling condition is superfluous for the most part of the classical theory; see [2,[8][9][10][11]14] and their references. The analysis with non-doubling measures is proved to play a striking role in solving the long-standing open Painlevé's problem by Tolsa [13]; see also [15] for more background of analysis with non-doubling measures.…”