2014/03/20 by Thaís Jordão, Jordão, Thaís, V. A. Menegatto +2
Mathematics · #42B05 and 47A75 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #math.FA #msc:42B05 #msc:47A75
paper · pdf · doi:10.48550/arxiv.1403.5213
15 pages
arxiv created 2014/03/20 · openalex publication_date 2014/03/20 · arxiv updated 2014/03/21 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We provide estimates for weighted Fourier sums of integrable functions defined on the sphere when the weights originate from a multiplier operator acting on the space where the function belongs. That implies refined estimates for weighted Fourier sums of integrable kernels on the sphere that satisfy an abstract Hölder condition based on a parameterized family of multiplier operators defining an approximate identity. This general estimation approach includes an important class of multipliers operators, namely, that defined by convolutions with zonal measures. The estimates are used to obtain decay rates for the eigenvalues of positive integral operators on L2(Sm) and generated by a kernel satisfying the Hölder condition based on multiplier operators on L2(Sm).