A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa

By Tuomas Hytönen. 2009

127 citations recorded by the source corpus.

A new class of metric measure spaces is introduced and studied. This class generalises the well-established doubling metric measure spaces as well as the spaces (R, μ) with μ(B(x, r)) ≤ Cr, in which non-doubling harmonic analysis has recently been developed. It seems to be a promising framework for an abstract extension of this theory. Tolsa’s space of regularised BMO functions is defined in this new setting, and the John-Nirenberg inequality is proven.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/a97aeb926af7ff2a1ba6da5fcc801b516eccd6b2

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In Astronomy and Astrophysics

1. Dachun Yang
2. Dongyong Yang
3. Wen Yuan
4. Xing Fu
5. Suile Liu
6. Juha Kinnunen
7. Tuomas Hytönen

Citations in the corpus

• Maximal Function Methods for Sobolev Spaces (2021, background): “174, American Mathematical Society, Providence, RI, 1998. Translated from the 1991 Chinese original by Bei Hu. MR1616087 [83] Filippo Chiarenza and Michele Frasca, A note on a weighted Sobolev inequality, Proc. Amer. Math. Soc. 93 (1985), no. 4, 703–704. MR776206 [84] Filippo Chiarenza and Michele F”
• Boundedness of Calderón–Zygmund Operators on Non-homogeneous Metric Measure Spaces (2010, methodology): “In [9], Hytönen introduced a new class of metric measure spaces satisfying the so-called upper doubling condition and the geometrical doubling condition (see also Definitions 1.”
• GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES (2013, methodology): “In [18], Hytönen showed that the following statements are mutually equivalent: (i) (X , d) is geometrically doubling.”