A note on the M. Riesz theorem for the conjugate function

• Autorzy: Papadopoulos S.
• Języki publikacji: EN

Abstrakty

EN

In this note we shall prove that if p is a power of 2, i.e. p = 2[sup k], k [belongs to] N, and f(0) = 0, that is f has the Fourier series Sigma[...] with a[sub o] = 0, then [...].

Słowa kluczowe

EN

conjugate function; Fourier analysis; M. Riesz inequality

PL

analiza Fouriera; funkcja sprzężona

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 3
• Strony: 283--288
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Papadopoulos S.

• Lefkados 502, Liani Amos, 341 00 Halkida, Greece

Bibliografia

• [1] A. Baernstein, H, S. J. Montgomery-Smith, Some conjectures about integral means of δf and δf, 79 , preprint
• [2] A. P. Calderon, On theorems of M. Riesz and Zygmund, Proc. Amer. Math. Soc., 1 (1950) 533-535.
• [3] I. Ts. Gohberg, N. Ya. Krupnik, Norm of the Hilbert transformation in the LP space, Funct. Anal. Appl. 2.2 (1968) 180-181 (translated from the Russian).
• [4] M. Essen, A superharmonic proof of the M. Riesz conjugate function theorem, Ark. Mat., 22 (1984) 241-249.
• [5] N. Ya. Krupnik, I. E. Verbitsky, The norm of the Riesz projection, in: Linear and complex analysis problem book 3, Part I, eds.: V. P. Havin and N. K. Nikolski, Lect. Notes Math., Springer-Verlag, 1543 (1994) 422-423.
• [6] A. Pełczyński, Norms of classical opearators in function spaces, Colloque Laurent Schwartz, Asterisque, 131 (1985) 137-162.
• [7] S. K. Pichorides, On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov, Studia Math., 44 (1972) 165-179.
• [8] M. Riesz, Sur les fonctions conjugućes, Math. Z., 27 (1927) 218-244.
• [9] P. Stein, On a theorem of M. Riesz, J. London Math. Soc., 8 (1933) 242-247.
• [10] I. E. Verbitskii, An estimate of the norm of a function in Hardy space in terms of the norms of its real and imaginary parts (in Russian), Mat. Issled. Vyp., 54 (1980) 16-20 and in Amer. Math. Soc. Transl. 124 (2) (1984) 11-15.
• [11] V. Yudin, On Fourier sums in LP, Proc. Steklov Inst. Math., 178 (1989) 279-280.
• [12] A. Zygmund, Trigonometric Series, I and II, Cambridge Univ. Press, 2nd Edition, 1968.