Adaptive Deterministic Dyadic Grids on Spaces of Homogeneous Type

• Autorzy: Lechner R. , Passenbrunner M.

Identyfikatory

DOI

10.4064/ba62-2-4

• Języki publikacji: EN

Abstrakty

EN

In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector-valued operators rearranging martingale difference sequences such as the Haar system.

Słowa kluczowe

EN

space of homogeneous type; vector valued; UMD; adaptive dyadic grid; rearrangement operator; stripe operator; martingale difference sequence

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no 2
• Strony: 139--159
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Lechner R.

• Institute of Analysis Johannes Kepler University Linz Altenberger Strasse 69 A-4040 Linz, Austria

autor

Passenbrunner M.

• Institute of Analysis Johannes Kepler University Linz Altenberger Strasse 69 A-4040 Linz, Austria

Bibliografia

• [1] S. Y. A. Chang, J. M. Wilson, and T. H. Wolff, Some weighted norm inequalities concerning the Schrödinger operators, Comment. Math. Helv. 60 (1985), 217–246.
• [2] M. Christ, A T(b) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61 (1990), 601–628.
• [3] G. David, Wavelets and Singular Integrals on Curves and Surfaces, Lecture Notes in Math. 1465, Springer, Berlin, 1991.
• [4] B. Davis, Hardy spaces and rearrangements, Trans. Amer. Math. Soc. 261 (1980), 211–233.
• [5] 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.
• [6] 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.
• [7] J. B. Garnett and P. W. Jones, BMO from dyadic BMO, Pacific J. Math. 99 (1982), 351–371.
• [8] T. P. Hytönen, Vector-valued singular integrals revisited—with random dyadic cubes, Bull. Polish Acad. Sci. Math. 60 (2012), 269–283.
• [9] R. Lechner, An interpolatory estimate for the UMD-valued directional Haar projection, Dissertationes Math. 503 (2014), 60 pp.
• [10] R. Lechner, The one-third-trick and shift operators, Bull. Polish Acad. Sci. Math. 61 (2013), 219–238.
• [11] 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.
• [12] R. A. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. Math. 33 (1979), 257–270.
• [13] P. F. X. Müller and M. Passenbrunner, A decomposition theorem for singular integral operators on spaces of homogeneous type, J. Funct. Anal. 262 (2012), 1427–1465.
• [14] S. Müller, Rank-one convexity implies quasiconvexity on diagonal matrices, Int. Math. Res. Notices 1999, 1087–1095.
• [15] F. Nazarov, S. Treil, and A. Volberg, Cauchy integral and Calderón–Zygmund operators on nonhomogeneous spaces, Int. Math. Res. Notices 1997, 703–726.
• [16] F. Nazarov, S. Treil, and A. Volberg, The Tb-theorem on non-homogeneous spaces, Acta Math. 190 (2003), 151–239.
• [17] T. H. Wolff, Two algebras of bounded functions, Duke Math. J. 49 (1982), 321–328.