2024/10/02 by Tomasz Kiwerski, Kiwerski, Tomasz, Jakub Tomaszewski +1
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2410.01420
openalex publication_date 2024/10/02 · openalex created_date 2024/10/30 · openalex updated_date 2026/07/28
We will provide a complete description of the space M(XF,XG) of pointwise multipliers between two Calderón--Lozanovskiĭ spaces XF and XG built upon a rearrangement invariant space X and two Young functions F and G. Meeting natural expectations, the space M(XF,XG) turns out to be another Calderón--Lozanovskiĭ space XG \ominus F with G \ominus F being the appropriately understood generalized Young conjugate of G with respect to F. Nevertheless, our argument is not a mere transplantation of existing techniques and requires a rather delicate analysis of the interplay between the space X and functions F and G. Furthermore, as an example to illustrate applications, we will solve the factorization problem for Calderón--Lozanovskiĭ spaces. All this not only complements and improves earlier results (basically giving them the final touch), but also confirms the conjecture formulated by Kolwicz, Leśnik and Maligranda in [Pointwise multipliers of Calderón--Lozanovskiĭ spaces, Math. Nachr. 286 (2012), no. 8-9, 876--907]. We will close this work by formulating a number of open questions that outline a promising panorama for future research.