Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 811–823

REGULARIZATION FOR LOZANOVSKII'S TYPE FACTORIZATION WITH APPLICATIONS

Karol Leśnik, Lech Maligranda and Pawel Mleczko

Poznan University of Technology, Institute of Mathematics
ul. Piotrowo 3a, 60-965 Poznan, Poland; klesnik 'at' vp.pl

Luleå University of Technology, Department of Engineering Sciences and Mathematics
SE-971 87 Luleå, Sweden; lech.maligranda 'at' ltu.se

Adam Mickiewicz University in Poznan, Faculty of Mathematics and Computer Science
ul. Uniwersytetu Poznanskiego 4, 61-614 Poznan, Poland; pml 'at' amu.edu.pl

Abstract. We say that a function space Z is factorable by X when there exists a third function space Y such that each f from Z admits factorization f = gh, where g, h belong to X, Y, respectively, and ||f||_Z ≈ ||g||_X||h||_Y. We consider a problem of regularization of such a factorization; namely, suppose that f like above satisfies some additional regularity condition (i.e., is holomorphic, smooth or is a simple function). May g, h be chosen to have the same property? Answer to such a question when f is holomorphic leads us to factorization of Hardy type spaces. We also apply these considerations to get factorization for Toeplitz operators on Hardy spaces.

2010 Mathematics Subject Classification: Primary 46E30, 46E15; Secondary 42B30, 46J15, 47B35.

Key words: Symmetric spaces, Hardy spaces, Toeplitz operators, factorization.

Reference to this article: K. Leśnik, L. Maligranda and P. Mleczko: Regularization for Lozanovskii's type factorization with applications. Ann. Acad. Sci. Fenn. Math. 45 (2020), 811–823.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4545