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Algebra i Analiz, 2006, Volume 18, Issue 2, Pages 24–56 (Mi aa67)  

This article is cited in 33 scientific papers (total in 33 papers)

Research Papers

The Bellman functions for a certain two-weight inequality: A case study

V. Vasyunina, A. Vol'bergb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Department of Mathematics, Michigan State University, MI, USA
References:
Abstract: A formula is presented for the exact Bellman function of a certain “toy” two-weight problem. This adds one more function to a short list of other Bellman functions for which the precise expressions have recently been found. The case study reveals essential features of finding Bellman functions in general and gives the extremal sequences for the problem. Some open questions are posed.
Received: 30.11.2005
English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 2, Pages 201–222
DOI: https://doi.org/10.1090/S1061-0022-07-00953-3
Bibliographic databases:
Document Type: Article
MSC: 42B20, 42A50, 47B35
Language: Russian
Citation: V. Vasyunin, A. Vol'berg, “The Bellman functions for a certain two-weight inequality: A case study”, Algebra i Analiz, 18:2 (2006), 24–56; St. Petersburg Math. J., 18:2 (2007), 201–222
Citation in format AMSBIB
\Bibitem{VasVol06}
\by V.~Vasyunin, A.~Vol'berg
\paper The Bellman functions for a certain two-weight inequality: A~case study
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 2
\pages 24--56
\mathnet{http://mi.mathnet.ru/aa67}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2244935}
\zmath{https://zbmath.org/?q=an:1125.47025}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 2
\pages 201--222
\crossref{https://doi.org/10.1090/S1061-0022-07-00953-3}
Linking options:
  • https://www.mathnet.ru/eng/aa67
  • https://www.mathnet.ru/eng/aa/v18/i2/p24
  • This publication is cited in the following 33 articles:
    1. Osekowski A. Rapicki M., “Sharp Lorentz-Norm Estimates For Dyadic-Like Maximal Operators”, Studia Math., 257:1 (2021), 87–110  crossref  mathscinet  isi
    2. Nikolidakis E.N., “A Sharp Integral Inequality For the Dyadic Maximal Operator and a Related Stability Result”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 45 (2020), 533–546  crossref  mathscinet  isi  scopus
    3. Delis A.D. Nikolidakis E.N., “Sharp Integral Inequalities For the Dyadic Maximal Operator and Applications”, Math. Z., 291:3-4 (2019), 1197–1209  crossref  mathscinet  zmath  isi  scopus
    4. Melas A.D., “An Eigenfunction Stability Estimate For Approximate Extremals of the Bellman Function For the Dyadic Maximal Operator on l-P”, Proc. Amer. Math. Soc., 147:8 (2019), 3367–3375  crossref  mathscinet  isi  scopus
    5. Nikolidakis E.N., “Extremal Sequences For the Bellman Function of Three Variables of the Dyadic Maximal Operator Related to Kolmogorov'S Inequality”, Trans. Am. Math. Soc., 372:9 (2019), 6315–6342  crossref  mathscinet  isi  scopus
    6. Delis A.D. Nikolidakis E.N., “Sharp and General Estimates For the Bellman Function of Three Integral Variables Related to the Dyadic Maximal Operator”, Colloq. Math., 153:1 (2018), 27–37  crossref  mathscinet  zmath  isi  scopus
    7. Melas A.D. Nikolidakis E.N., “Sharp Lorentz Estimates For Dyadic-Like Maximal Operators and Related Bellman Functions”, J. Geom. Anal., 27:4 (2017), 2644–2657  crossref  mathscinet  zmath  isi  scopus
    8. Nikolidakis E.N., “Extremal Sequences For the Bellman Function of the Dyadic Maximal Operator and Applications to the Hardy Operator”, Can. J. Math.-J. Can. Math., 69:6 (2017), 1364–1384  crossref  mathscinet  zmath  isi  scopus
    9. Melas A.D. Nikolidakis E.N., “Local Lower Norm Estimates For Dyadic Maximal Operators and Related Bellman Functions”, J. Geom. Anal., 27:3 (2017), 1940–1950  crossref  mathscinet  zmath  isi  scopus
    10. Nikolidakis E.N., “the Bellman Function of the Dyadic Maximal Operator Related to Kolmogorov'S Inequality”, Isr. J. Math., 219:2 (2017), 507–528  crossref  mathscinet  zmath  isi  scopus
    11. Melas A.D. Nikolidakis E.N. Cheliotis D., “Estimates For Bellman Functions Related to Dyadic-Like Maximal Operators on Weighted Spaces”, Studia Math., 239:1 (2017), 1–16  crossref  mathscinet  zmath  isi  scopus
    12. Janakiraman P. Volberg A., “New Bellman Functions and Subordination By Orthogonal Martingales in l-P, 1 < P <= 2”, Harmonic Analysis, Partial Differential Equations and Applications: in Honor of Richard l. Wheeden, Applied and Numerical Harmonic Analysis, ed. Chanillo S. Franchi B. Lu G. Perez C. Sawyer E., Springer International Publishing Ag, 2017, 239–273  crossref  mathscinet  zmath  isi  scopus
    13. Slavin L., “Best Constants For a Family of Carleson Sequences”, Adv. Math., 289 (2016), 685–724  crossref  mathscinet  zmath  isi  elib  scopus
    14. Ivanisvili P. Osipov N.N. Stolyarov D.M. Vasyunin V.I. Zatitskiy P.B., “Bellman function for extremal problems in BMO”, Trans. Am. Math. Soc., 368:5 (2016), 3415–3468  crossref  mathscinet  zmath  isi  elib  scopus
    15. Osekowski A., “Sharp Estimates for Lipschitz Class”, J. Geom. Anal., 26:2 (2016), 1346–1369  crossref  mathscinet  zmath  isi  scopus
    16. Osekowski A., “Sharp Logarithmic Inequalities for Hardy Operators”, Z. Anal. ihre. Anwend., 35:1 (2016), 1–20  crossref  mathscinet  zmath  isi  scopus
    17. Stolyarov D.M. Zatitskiy P.B., “Theory of locally concave functions and its applications to sharp estimates of integral functionals”, Adv. Math., 291 (2016), 228–273  crossref  mathscinet  zmath  isi  elib  scopus
    18. Nikolidakis E.N. Melas A.D., “A Sharp Integral Rearrangement Inequality For the Dyadic Maximal Operator and Applications”, Appl. Comput. Harmon. Anal., 38:2 (2015), 242–261  crossref  mathscinet  zmath  isi  elib  scopus
    19. Osekowski A., “A Splitting Procedure For Bellman Functions and the Action of Dyadic Maximal Operators on l-P”, Mathematika, 61:1 (2015), 199–212  crossref  mathscinet  zmath  isi  scopus
    20. Ivanisvili P. Osipov N.N. Stolyarov D.M. Vasyunin V.I. Zatitskiy P.B., “Sharp Estimates of Integral Functionals on Classes of Functions With Small Mean Oscillation”, C. R. Math., 353:12 (2015), 1081–1085  crossref  mathscinet  zmath  isi  elib  scopus
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    Алгебра и анализ St. Petersburg Mathematical Journal
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