Non-similarity of Walsh and trigonometric systems

• Autorzy: P. Wojtaszczyk
• Języki publikacji: EN

Abstrakty

EN

We show that in $L_p$ for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 142
• Numer: 2
• Strony: 171-185

Daty

wydano

2000

otrzymano

2000-01-12

poprawiono

2000-06-20

Twórcy

autor

P. Wojtaszczyk

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] R. A. DeVore and G. G. Lorentz, Constructive Approximation, Springer, Berlin, 1993.
• [2] D. Jackson, Certain problems in closest approximation, Bull. Amer. Math. Soc. 39 (1933), 889-906.
• [3] A. Pietsch and J. Wenzel, Orthonormal Systems and Banach Space Geometry, Cambridge Univ. Press, Cambridge 1998.
• [4] F. Schipp, W. R. Wade and P. Simon, Walsh Series--an Introduction to Dyadic Harmonic Analysis, Akadémiai Kiadó, Budapest, 1990.
• [5] W. S. Young, A note on Walsh-Fourier series, Proc. Amer. Math. Soc. 59 (1976), 305-310.
• [6] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, Cambridge, 1959.