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Best constant in Zygmund's inequality and related estimates for orthogonal harmonic functions and martingales

Adam Osekowski
대한수학회 (The Korean Mathematical Society)|2012.05|대한수학회지 (Journal of the KMS)|제49권 제3호|pp. 659-670|DOI http://dx.doi.org/

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참고문헌

키워드

martingaleharmonic functiondifferential subordinationbest constantsLlogL inequality
주제분류수학

초록

Abstract. For any K > 2/π we determine the optimal constant L(K)for which the following holds. If u, ~u are conjugate harmonic functions on the unit disc with u(0) = 0, then 수식We also establish a related estimate for orthogonal harmonic functions given on Euclidean domains as well as an extension concerning orthogonal martingales under differential subordination.

Abstract

Abstract. For any K > 2/π we determine the optimal constant L(K)for which the following holds. If u, ~u are conjugate harmonic functions on the unit disc with u(0) = 0, then 수식We also establish a related estimate for orthogonal harmonic functions given on Euclidean domains as well as an extension concerning orthogonal martingales under differential subordination.

참고문헌 (17)

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  3. R. Banuelos, "Davis's inequality for orthogonal martingales under differential subordination", Michigan Math. J, 47(1), pp.109~124 (2000)
  4. D. L. Burkholder, "Differential subordination of harmonic functions and martingales, Harmonic analysis and partial differential equations", Lecture Notes in Math, 1384, pp.1~23 (1989), Springer
  5. C. Dellacherie, "Probabilities and Potential B" (1982), NorthHolland
  6. M. Essen, "Best constants in Zygmund's inequality for conjugate functions, Papers on analysis", Rep. Univ. Jyvaskyla Dep. Math. Stat, 83, pp.73~80 (2001), University of Jyvaskila
  7. M. Essen, "Sharp Llogfl L inequalities for conjugate functions", Ann. Inst. Fourier (Greno- ble), 52(2), pp.623~659 (2002)
  8. T. W. Gamelin, "Uniform Algebras and Jensen Measures, London Math. Soc. Lecture Notes Series, Vol. 32" (1978), Cambridge Univ. Press
  9. P. Janakiraman, "Best weak-type (p; p) constants, 1 < p < 2, for orthogonal harmonic functions and martingales", Illinois J. Math, 48(3), pp.909~921 (2004)
  10. A. Osekowski, "Sharp inequalities for differentially subordinate harmonic functions and martingales", Canadian Math. Bull
  11. G. Peskir, "Optimal Stopping and Free Boundary Problems, In Lectures in Mathematics ETH Zurich" (2006), Birkhauser Verlag
  12. S. K. Pichorides, "On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov", Studia Math, 44, pp.165~179 (1972)
  13. M. Riesz, "Les fonctions conjugees et ler series de Fourier", C. R. Acad. Paris, 178, pp.1464~1467 (1924)
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  15. D. Revuz, "Continuous Martingales and Brownian Motion, 3rd edition" (1999), Springer Verlag
  16. G.Wang, "Differential subordination and strong differential subordination for continuous time martingales and related sharp inequalities", Ann. Probab, 23(2), pp.522~551 (1995)
  17. A. Zygmund, "Sur les fonctions conjugees", Fund. Math, 13, pp.284~303 (1929)

관련 논문AI추천

ON Φ-INEQUALITIES FOR BOUNDED SUBMARTINGALES AND SUBHARMONIC FUNCTIONSAdam Osekowski대한수학회 · 대한수학회논문집2008 · 제23권 제2호Remarks on weighted harmonic Bergman functions on half-spaces이흥수장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제3호ON HARMONICITY IN A DISC AND n-HARMONICITY이재성대한수학회 · 대한수학회보2010 · 제47권 제4호BERGMAN SPACES, BLOCH SPACES AND INTEGRAL MEANS OF p-HARMONIC FUNCTIONSJinjing Qiao, Xi Fu대한수학회 · 대한수학회보2021 · 제58권 제2호WEIGHED HARMONIC BERGMAN FUNCTIONS AS RADIAL DERIVATIVES OF BERGMAN FUNCTIONS ON HALF-SPACES위형수장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2010 · 제13권 제1호On M-subharmonicity in the ball권언근, 박종희대한수학회 · 대한수학회논문집2013 · 제28권 제3호

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