79
Views
0
CrossRef citations to date
0
Altmetric
Articles

Sharp estimates for holomorphic functions on the unit ball of ℂn

Pages 323-332 | Received 16 Mar 2014, Accepted 25 May 2014, Published online: 27 Jun 2014

References

  • Riesz M. Sur les fonctions conjugées [On conjugate harmonic functions]. Math. Z. 1927;27:218–244.
  • Gohberg I, Krupnik N. Norm of the Hilbert transformation in the Lp space. Funct. Anal. Pril. 1968;2:91–92. Russian. English transl. in Funct. Anal. Appl. 1968;2:180–181.
  • Pichorides SK. On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov. Studia Math. 1972;44:165–179.
  • Gamelin TW. Uniform algebras and Jensen measures. London: Cambridge University Press; 1978.
  • Essén EM. A superharmonic proof of the M. Riesz conjugate function theorem. Ark. Mat. 1984;22:241–249.
  • Verbitsky IE. Estimate of the norm of a function in a Hardy space in terms of the norms of its real and imaginary part. Mat. Issled. 1980;54:16–20. Russian. English transl. in Amer. Math. Soc. Transl. 1984;124:11–15.
  • Pełczyński A. Norms of classical operators in function spaces. In: Colloque en l’honneur de Laurent Schwartz. Vol. 1. Asterisque. 1985;131:137–162.
  • Hollenbeck B, Verbitsky IE. Best constants for the Riesz projection. J. Funct. Anal. 2000;175:370–392.
  • Hollenbeck B, Verbitsky IE. Best constant inequalities involving the analytic and co-analytic projections. Oper. Theory Adv. Appl. 2010;202:285–296.
  • Davis B. On the weak (1,1) inequality for conjugate functions. Proc. Amer. Math. Soc. 1974;4:307–311.
  • Janakiraman P. Best weak-type (p, p) constants, 1 ≤ p ≤ 2 for orthogonal harmonic functions and martingales. Illinois J. Math. 2004;48:909–921.
  • Kolmogorov AN. Sur les fonctions harmoniques conjugées et les séries de Fourier [On conjugate harmonic functions and Fourier series]. Fund. Math. 1925;7:24–29.
  • Osȩkowski A. Sharp inequalities for differentially subordinate harmonic functions and martingales. Canadian Math. Bull. 2012;55:597–610.
  • Osȩkowski A. Sharp weak type inequalities for Hilbert transform and Riesz projection. Israel J. Math. 2012;192:429–448.
  • Tomaszewski B. The best constant in a weak-type H1-inequality, complex analysis and its applications. Complex Var. 1984;4:35–38.
  • Tomaszewski B. Some sharp weak-type inequalities for holomorphic functions on the unit ball of ℂn. Proc. Amer. Math. Soc. 1985;95:271–274.
  • Gohberg I, Krupnik N. One-dimensional linear singular integral equations. Vol. I, II, Operator theory: advances and applications. Basel: Birkhäuser; 1992.
  • Krupnik N. Survey on the best constants in the theory of one-dimensional singular integral operators. Oper. Theory Adv. Appl. 2010;202:365–393.
  • Zygmund A. Trigonometric series. London: Cambridge University Press; 1968.
  • Rudin W. Function theory in the unit ball of ℂn. New York (NY): Springer-Verlag; 1980.
  • Range RM. Holomorphic functions and integral representations in several complex variables. Vol. 108, Graduate texts in mathematics. New York (NY): Springer-Verlag; 1986.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.