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We first determine when the sum of products of Hankel and Toeplitz operators is equal to zero; then we characterize when the product of a Toeplitz operator and a Hankel operator is a compact perturbation of a Hankel operator or a Toeplitz operator and when it is a finite rank perturbation of a Toeplitz operator.
In this article, via fractional Hajłasz gradients, the authors introduce a class of fractional Hajłasz-Morrey-Sobolev spaces, and investigate the relations among these spaces, (grand) Morrey-Triebel-Lizorkin spaces and Triebel-Lizorkin-type spaces on both Euclidean spaces and RD-spaces.
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