In this paper we introduce Calder\'on-Zygmund theory for singular stochastic integrals with operator-valued kernel. particular, prove $L^p$-extrapolation results under a H\"ormander condition on the Sparse domination and sharp weighted bounds are obtained Dini kernel, leading to version of solution $A_2$-conjecture. The applied obtain $p$-independence maximal $L^p$-regularity both in complex re...

In this paper, we introduce two classes of localized integral operators on L2(Rd) with the Wiener class W and the Kurbatov class K of integral operators as their models. We show that those two classes of localized integral operators are pseudo-inverse closed non-unital subalgebra of B2, the Banach algebra of all bounded operators on L2(Rd) with usual operator norm.

As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [4, 5, 6, 7, 8, 9, 10]). In [4, 5, 6, 7, 8, 9, 10], the authors prove that the commutators and multilinear operators generated by the singular integral operators and BMO functions are bounded on L(R) for 1 < p <∞; Chanillo (see [2]) proves a similar result when singular int...

It is well known that solutions of inhomogeneous differential and integral equations are represented by integral operators. To investigate the stability of solutions, we often use the continuity of corresponding integral operators in the studied function spaces. For instance, the boundedness of Fourier multiplier operators plays a crucial role in the theory of linear PDE’s, especially in the st...

We study some integral operators and determine conditions for the univalence of these integral operators.