Essential norms of composition operators between Bloch type spaces in the polydisk

New Characterizations of Composition Operators Between Bloch Type Spaces in the Unit Ball

“…For the higher dimensional case, in 2012, the authors in [6] generalize Zhao's results in [19] to the polydisk. Unlike the case of composition operators on the unit disk, the essential norms are different for the cases p ∈ (0, 1) and p ≥ 1.…”

Essential norms of the integral-type composition operators between Bloch-type spaces

“…Where the notation {e n } is the function sequence defined in the unit disk D as e n (z) = z n . Subsequently to this, several authors have extended the results to the differentiation composition operators and weighted composition operators, one can refer to [11][12][13][14][15][16]. In this paper, we are interested in the problem: whether the result still holds about the integer-type operators between the Bloch-type spaces.…”

New characterizations for differences of weighted differentiation composition operators from a Bloch-type space to a weighted-type space

“…As we all know, B α is a Banach space endowed with the norm f B α , and the little Bloch-type space B α 0 is the closure of polynomials in B α , see,e.g. [3,5,10,11,16]. More generally, let v be a strictly positive continuous and bounded function (weight) on D. The weighted-type space H ∞ v is defined to be the collection of all functions f ∈ H(D) that satisfy…”