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http://dx.doi.org/10.4134/CKMS.c200095

DIFFERENCES OF DIFFERENTIAL OPERATORS BETWEEN WEIGHTED-TYPE SPACES  

Al Ghafri, Mohammed Said (Department of Mathematics Sultan Qaboos University)
Manhas, Jasbir Singh (Department of Mathematics Sultan Qaboos University)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.3, 2021 , pp. 465-483 More about this Journal
Abstract
Let 𝓗(𝔻) be the space of analytic functions on the unit disc 𝔻. Let 𝜓 = (𝜓j)nj=0 and 𝚽 = (𝚽j)nj=0 be such that 𝜓j, 𝚽j ∈ 𝓗(𝔻). The linear differential operator is defined by T𝜓(f) = ∑nj=0 𝜓jf(j), f ∈ 𝓗(𝔻). We characterize the boundedness and compactness of the difference operator (T𝜓 - T𝚽)(f) = ∑nj=0 (𝜓j - 𝚽j) f(j) between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (non compact) differential operators such that their difference is bounded (compact).
Keywords
Difference operators; differential operators; multiplication operators; weighted-type spaces; Bloch-type spaces; bounded and compact operators;
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