Combinatorics of Dyadic Intervals : Consistent Colourings

• Autorzy: Kamont A. , Müller P. F. X.

Identyfikatory

DOI

10.4064/ba62-2-1

• Języki publikacji: EN

Abstrakty

EN

We study the problem of consistent and homogeneous colourings for increasing families of dyadic intervals. We determine when this problem can be solved and when it cannot.

Słowa kluczowe

EN

coloured dyadic intervals; consistent and homogeneous colouring; 2-person games

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no 2
• Strony: 101--115
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Kamont A.

• Institute of Mathematics Polish Academy of Sciences Wita Stwosza 57 80-952 Gdańsk, Poland

autor

Müller P. F. X.

• Department of Analysis J. Kepler University A-4040 Linz, Austria

Bibliografia

• [1] T. Figiel, On equivalence of some bases to the Haar system in spaces of vector-valued functions, Bull. Polish Acad. Sci. Math. 36 (1988), 119-131.
• [2] T. Figiel, Singular integral operators: a martingale approach, in: Geometry of Banach Spaces (Strobl, 1989), London Math. Soc. Lecture Note Ser. 158, Cambridge Univ. Press, Cambridge, 1990, 95-110.
• [3] J. B. Garnett, Bounded Analytic Functions, Pure Appl. Math. 96, Academic Press, New York, 1981.
• [4] P. W. Jones, Carleson measures and the Fefferman-Stein decomposition of BMO(R), Ann. of Math. (2) 111 (1980), 197-208.
• [5] P. W. Jones, BMO and the Banach space approximation problem, Amer. J. Math. 107 (1985), 853-893.
• [6] A. Kamont and P. F. X. Müller, Rearrangements with supporting trees, isomorphisms and shift operators, Math. Z. 274 (2013), 57-83.
• [7] J. Lee, P. F. X. Müller and S. Müller, Compensated compactness, separately convex functions and interpolatory estimates between Riesz transforms and Haar projections, Comm. Partial Differential Equations 36 (2011), 547-601.
• [8] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II. Function Spaces, Ergeb. Math. Grenzgeb. 97, Springer, Berlin, 1979.
• [9] P. F. X. Müller, Rearrangements of the Haar system that preserve BMO, Proc. London Math. Soc. (3) 75 (1997), 600-618.
• [10] P. F. X. Müller, Isomorphisms between H1 Spaces, IMPAN Monogr. Mat. (N.S.) 66, Birkhäuser, Basel, 2005.
• [11] K. Smela, Continuous rearrangements of the Haar system in Hp for 0 < p < 1, Studia Math. 189 (2008), 189-199.
• [12] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Ann. of Math. Stud. 63, Princeton Univ. Press, Princeton, NJ, and Univ. of Tokyo Press, Tokyo, 1970.