Lectures on Analysis on Metric Spaces

By J. Heinonen. 2000

1,430 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c3c1b215c725743584a706929055b62be10fc648

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

POTENTIAL THEORY OF QUASIMINIMIZERS (2003, background): “where N depends only on the doubling constant, see [ He ].”
Quasi-hyperbolic planes in hyperbolic groups (2003, background): “By de nition a quasi-circle is a metric circle which admits a quasisymmetric parametrization by the unit circle S1 R2 (see [10] for the de nition and basic facts about quasisymmetric maps).”
Moser iteration for (quasi)minimizers on metric spaces (2006, background): “Let A be the set of non-Lebesgue points of u, which has measure 0, see, e.g., Heinonen [ 21 ], Theorem 1.8.”
Random Martingales and localization of maximal inequalities (2009, background): “It is a classical fact, due to Vol′berg and Konyagin [54] in the case of compact spaces, and Luukkainen and Saksman [33] in the case of general complete spaces (see also [55] and chapter 13 in [27]), that X admits a non-degenerate measure μ which is doubling with constant λ(2) (the power 2 can be re”
Maximal function characterizations of Hardy spaces on RD-spaces and their applications (2008, background): “Structures of spaces of homogeneous type encompass several important examples in harmonic analysis, such as Euclidean spaces with A∞-weights (of the Muckenhoupt class), Ahlfors nregular metric measure spaces (see, for example, [ 11 , 12]), Lie groups of polynomial growth (see, for instance, [13–15])”
Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group (2009, background): “This last setting has proved to be very efficient as a minimal framework permitting to generalize conformal geometry to some metric measure spaces (see [13] and the references therein).”
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, methodology): “ (X,dE,µ) satisﬁes the volume doubling property if there exists a constant C > 0 such that for every x ∈ X and r > 0, µ(B(x,2r)) ≤ C µ(B(x,r)). 5 It follows from the doubling property of µ (see [42]) that there is a constant 0 < Q < ∞ and C ≥ 1 such that whenever 0 < r ≤ R and x ∈ X, ”
A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa (2009, neutral): “[10], [11]).”
Variable exponent Sobolev spaces on metric measure spaces (2006, background): “Sobolev spaces on metric measure spaces have been studied very intensively during the last ten years, and the ”standard” framework is now available in the monograph [18] by J.”