Boundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, II

Compactness of Commutators of Riesz Potential on Morrey Spaces

“…In fact, the authors of [10] and [11] have applied commutator theory to give a compactness characterization of Hankel operators on holomorphic Hardy spaces H 2 (D), where D is a bounded, strictly pseudoconvex domain in C n . It is perhaps for this important reason that the compactness of [b , T] attracted one's attention among researchers in PDEs.…”

“…Boundedness and compactness characterization for [b , T] on L p space over some spaces of homogeneous type was proved by Beatrous and Li [1], and applications to Hankel-type operators on Bergman spaces were given by Krantz and Li in [10] and [11].…”

Boundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, I

“…Therefore, by Lemma 2.1, we can always choose a family of balls so that the above is true. However, most known examples of space of homogeneous type, especially the ones we consider in [KRL2], satisfy this condition.…”

“…Moreover, as applications, we formulate and prove characterization theorems (Theorems 2.2 and 2.4 in [KRL2]) for the boundedness and compactness of Hankel operators or commutators M f S on holomorphic Hardy spaces H 2 D , where D is a bounded, strictly pseudoconvex domain in n and S is the Szegö projection.…”

Toeplitz operators related to strongly singular Calderón-Zygmund operators

“…When b ∈ BMO, Krantz and Li [4] discussed the L p boundedness of T b on the homogeneous space. The commutator generated by a fractional integral operator and a locally integrable function b can be regarded as a special case of the generalized Toeplitz operator Θ b α0 = m j=1 (T j,1 M b I α0 T j,2 + T j, 3 4 ), where T j,1 are the Calderón-Zygmund operators or ±I, T j,2 , T j, 4 are the bounded linear operators on L p , T j, 3 …”