Norm and essential norm of an integral‐type operator from the logarithmic Bloch space to the Bloch‐type space on the unit ball

Abstract

We calculate norm and essential norm of an integral-type operator from the logarithmic Bloch space and the little logarithmic Bloch space to Bloch-type spaces on the unit ball of C n . We show that there is a one-parameter class of equivalent norms on the logarithmic Bloch space for which the norms can be calculated.

Essential norm of linear operators from general weighted‐type spaces to Banach spaces and some applications

“…We will also use this simple fact here. There has been some considerable interest in calculating and estimating essential norms of concrete linear operators between spaces of holomorphic functions of one and several variables in terms of the included symbols and parameters (see, e.g., previous works [22,23,27,28,[33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] and the related references therein).…”

Norms of a Product of Integral and Composition Operators between Some Bloch-Type Spaces

“…. Beside this, we present a formula for its essential norm, extending the results in [23]. We use some of the methods and ideas in [13,14,23,26].…”

“…One of the basic problems is the calculation of their norms and essential norms [18][19][20][37][38][39]. Some recent formulas for the norms can be found in [11][12][13][14]23,26,31].…”

“…To solve it, in [13], we had to change the weight (1 − |z| 2 ) α . The method also works in some other situations [23]. Here, we employ this idea to calculate the norm of…”