2023/02/08 by J. J. Betancor, Betancor, J. J., Estafanía D. Dalmasso +3
Mathematics · #42B15 #42B20 #42B25 #42B35 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2302.04356
openalex publication_date 2023/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper we introduce spaces of \textupBLO-type related to Laguerre polynomial expansions. We consider the probability measure on (0,∞) defined by dγα(x)=(2)/(Γ(α+1))e-x2x2α+1dx with α>-\frac12. For every a>0, the space \textupBLOa((0,∞),γα) consists of all those measurable functions defined on (0,∞) having bounded lower oscillation with respect to γα over an admissible family Ba of intervals in (0,∞). The space \textupBLOa((0,∞),γα) is a subspace of the space \textupBMOa((0,∞),γα) of bounded mean oscillation functions with respect to γα and Ba. The natural a-local centered maximal function defined by γα is bounded from \textupBMOa((0,∞),γα) into \textupBLOa((0,∞),γα). We prove that the maximal operator, the ρ-variation and the oscillation operators associated with local truncations of the Riesz transforms in the Laguerre setting are bounded from L^∞((0,∞),γα) into \textupBLOa((0,∞),γα). Also, we obtain a similar result for the maximal operator of local truncations for spectral Laplace transform type multipliers.