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Izvestiya: Mathematics, 1998, Volume 62, Issue 4, Pages 651–671
DOI: https://doi.org/10.1070/im1998v062n04ABEH000195 (Mi im195) 		 
Improved interpolation theorems for a class of linear operators

E. I. Berezhnoia, V. I. Burenkovb

a P. G. Demidov Yaroslavl State University
b Steklov Mathematical Institute, Russian Academy of Sciences
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DOI: https://doi.org/10.1070/im1998v062n04ABEH000195
Abstract: New interpolation theorems are formulated for the class of operators that map the cone of positive functions into the cone of monotonic decreasing functions. These theorems are based on the concept of the $K^c$-functional. A formula for calculating the $K^c$-functional for some pairs of spaces is suggested. An example of an interpolation pair of spaces is considered in which the cones obtained with the help of Peetre's $K$-functional are different from those obtained using the $K^c$-functional.
Received: 26.02.1997
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1998, Volume 62, Issue 4, Pages 3–24
DOI: https://doi.org/10.4213/im195
Bibliographic databases:
MSC: 46M35
Language: English
Original paper language: Russian
Citation: E. I. Berezhnoi, V. I. Burenkov, “Improved interpolation theorems for a class of linear operators”, Izv. RAN. Ser. Mat., 62:4 (1998), 3–24; Izv. Math., 62:4 (1998), 651–671
Citation in format AMSBIB
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:72
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