Corpus ID: 237572162

Fourier coefficients of functions in power-weighted $L_2$-spaces and conditionality constants of bases in Banach spaces

  title={Fourier coefficients of functions in power-weighted \$L\_2\$-spaces and conditionality constants of bases in Banach spaces},
  author={Jos{\'e} L. Ansorena},
We prove that, given 2 < p < ∞, the Fourier coefficients of functions in L2(T, |t| dt) belong to lp, and that, given 1 < p < 2, the Fourier series of sequences in lp belong L2(T, |t| dt). Then, we apply these results to the study of conditional Schauder bases and conditional almost greedy bases in Banach spaces. Specifically, we prove that, for every 1 < p < ∞ and every 0 ≤ α < 1, there is a Schauder basis of lp whose conditionality constants grow as (m)m=1, and there is an almost greedy basis… Expand


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