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Projections and unconditional bases in direct sums of ℓp SPACES, 0<p≤∞
(Wiley, 2021)
info:eu-repo/semantics/article,
We show that every unconditional basis in a finite direct sum ⊕p∈Aℓp , with A ⊂ (0,∞], splits into unconditional bases of each summand. This settles a 40 years old question raised in 'A. Ortyński, Unconditional bases in ...
Unconditional and quasi-greedy bases in L-p with applications to Jacobi polynomials Fourier series
(European Mathematical Society, 2019)
info:eu-repo/semantics/article,
We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in L-p does not converge unless p = 2. As a by-product of our work on quasi-greedy bases in L-p(µ), we ...