On the coexistence of convergence and divergence phenomena for integral averages and an application to the Fourier–Haar series

Let C , D ⊂ N be disjoint sets, and C = { 1 / 2 c : c ∈ C } , D = { 1 / 2 d : d ∈ D } . We consider the associate bases of dyadic, axis-parallel rectangles R C and R D . We give necessary and sufficient conditions on the sets C a n d D such that there is a positive function f ∈ L 1 ( [ 0 , 1 ) 2 ) s...

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Veröffentlicht in:	Analysis mathematica (Budapest) 2024-03, Vol.50 (1), p.149-187
Hauptverfasser:	Hirayama, M., Karagulyan, D.
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Convergence Divergence Fourier series Mathematics Mathematics and Statistics Rectangles Sequences Tiling
Online-Zugang:	Volltext
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