Grand and small spaces based on the Calderón’s construction
Berezhnoi E.I.
August 2025Birkhauser
Analysis and Mathematical Physics
2025#15Issue 4
We propose two general methods for defining grand and small spaces based on Calderón’s construction and prove some fundamental properties of these spaces. In particular, we give a complete description of associative spaces to general grand and small spaces. Our description allows us to give an exact answer to the question posed in [25]. We give some examples illustrating our constructions for spaces constructed on sets of finite and infinite measure.
Associate space , Banach ideal space , Fundamental function , Grand space , Small space
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Department of Mathematics, Yaroslavl State University, 14, Sovetskaya St, Yaroslavl, 150 000, Russian Federation
Institute of Mathematics and Mathematical Modeling, Puschkin St, Almaty, 050010, 125, Kazakhstan
Regional Mathematical Center of Southern Federal University, 105/42, Bolshaya Sadovaya, Rostov-on-Don, 344090, Russian Federation
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
Regional Mathematical Center of Southern Federal University
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