Open AccessGeneralized Hilbert series operators
Author(s) -
Jianjun Jin,
Shuan Tang
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2113577j
Subject(s) - mathematics , series (stratigraphy) , hilbert space , sequence (biology) , bounded function , norm (philosophy) , operator (biology) , pure mathematics , mathematical analysis , paleontology , biochemistry , chemistry , genetics , repressor , political science , transcription factor , gene , law , biology
In this note we study the generalized Hilbert series operator H?, induced by a positive Bore measure ? on [0,1), between weighted sequence spaces. We characterize the measures ? for which H? is bounded between different sequence spaces. Finally, for certain special measures, we obtain the sharp norm estimates of the operators and establish some new generalized Hilbert series inequalities with the best constant factors.