Θ-type Calderón-Zygmund operators with non-doubling measures

Commutators of multilinear strongly singular integrals on non-homogeneous metric measure spaces

“…The non-doubling measure space is a space equipped with a non-negative measure µ, where µ only needs to satisfy the polynomial growth condition, i.e., for all x ∈ R n and r > 0, there exist a constant C 0 > 0 and k ∈ (0, n] such that (1.1) µ(B(x, r)) ≤ C 0 r k , where B(x, r) = {y ∈ R n : |y − x| < r}. There are many important results in nondoubling measure spaces (see [14], [15], [31], [34], [35], [38], [39] and the references therein). And the analysis on non-doubling measures has important applications in solving the long-standing open Painlevé's problem (see [34]).…”

Boundedness for Commutators of Bilinearθ-Type Calderón-Zygmund Operators on Nonhomogeneous Metric Measure Spaces

“…Later, many researchers further studied the properties of this operator. We [17] obtained the boundedness of -type Calderón-Zygmund operator and commutators on nondoubling measure spaces. Ri et al [18,19] researched the boundedness of -type Calderón-Zygmund operator on Hardy spaces with nondoubling measures and nonhomogeneous metric measure spaces, respectively.…”

Multilinear fractional integral operators on non-homogeneous metric measure spaces

“…However non-doubling measure is a nonnegative measure µ only satisfies the polynomial growth condition, i.e., for all x ∈ X and r > 0, there exists a constant C > 0 and k ∈ (0, n] such that, µ(B(x, r)) ≤ C 0 r k , (1.1) where B(x, r) = {y ∈ X : |y − x| < r}. This brings rapid development in harmonic analysis (see [2,7,10,11,22,24,25,27]). As an important application, it is to solve the long-standing open Painlevé's problem (see [24]).…”