Singular integral operators on function spaces

Boundedness of rough integral operators on Triebel-Lizorkin spaces

“…We point out that Theorem 1.4 represents a generalization of Theorem 1 in [4]. Earlier results concerning the operator M Ω,q can be found in [5] and [16], among others.…”

“…For relevant results one may consult [5], [16], [6], [7], among others. For example, J. Chen and C. Zhang in [7] (see also [24]) proved the following:…”

Singular integral operators on product Triebel-Lizorkin spaces

“…They proved that in Theorem A, one only needs to assume that Ω satisfies the cancellation condition (1.2) for all k [α] (see also [1]). At the same time, in [5], Chen et al further studied the boundedness properties of T Ω,α (α > 0) on Triebel-Lizorkin spaces and established the following theorem.…”

Boundedness of Parabolic Singular Integrals and Marcinkiewicz Integrals on Triebel-Lizorkin Spaces

“…In this case, the operatorT is the classical singular integral operator of convolution type and whose boundedness in various function spaces has been well-studied by many authors, see [3,6,8,11,13,15,18]. Nagel and Rivière proved in [10] that if Ω ∈ C 1 (S n−1 ) and h ≡ 1, then the parabolic singular integral operator T is bounded on L p (R n ).…”