与截面相关的Morrey空间与奇异积分

In this paper, we define the Morrey spaces M_F~(p,q) (Rn) and the Campanato spaces E_F~(p,q) (R~n) associated with a family F of sections and a doubling measure μ, where F is closely related to the Monge-Amp`ere equation. Furthermore, we obtain the boundedness of the Hardy-Littlewood maximal function associated to F, Monge-Amp`ere singular integral operators and fractional integrals on M_F~(p,q)(R~n). We also prove that the Morrey spaces M_F~(p,q) (R~n)and the Campanato spaces E_F~(p,q) (R~n) are equivalent with 1 ≤ q ≤ p ∞.

Morrey Spaces Associated to the Sections and Singular Integrals

In this paper, we define the Morrey spaces $\mathcal M^{p,q}_\mathcal F(\mathbb R^n)$ and the Campanato spaces $\mathcal E^{p,q}_\mathcal F(\mathbb R^n)$ associated with a family $\mathcal F$ of sections and a doubling measure $\mu$, where $\mathcal F$ is closely related to the Monge-Amp\`ere equation. Furthermore, we obtain the boundedness of the Hardy-Littlewood maximal function associated to $\mathcal F,$ Monge-Amp\`ere singular integral operators and fractional integrals on $\mathcal M^{p,q}_\mathcal F(\mathbb R^n)$. We also prove that the Morrey spaces $\mathcal M^{p,q}_\mathcal F(\mathbb R^n)$ and the Campanato spaces $\mathcal E^{p,q}_\mathcal F(\mathbb R^n)$ are equivalent with $1\leq q\leq p<\infty$.