BMO for nondoubling measures

By Joan Mateu, P. Mattila, A. Nicolau, J. Orobitg. 2000

133 citations recorded by the source corpus.

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In Applied Mathematics

In Surgery

Citations in the corpus

The fall of the doubling condition in Calderón-Zygmund theory (2002, background): “and [T2]), Cotlar’s inequality for the maximal singular integral ([NTV1] and [T3]) and many others ([ MMNO ], [OP] and [GM]).”
A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa (2009, background): “594, footnote] pointed out that John and Nirenberg’s proof “can be adapted to spaces of homogeneous type”, and explicit proofs can be found in [2], [14], [15].”
H1 and BMO for certain locally doubling metric measures spaces (2009, background): “An important case in which µ is not even locally doubling is that of nondoubling measures of polynomial growth treated, for instance, in [38,44, 46], where new spaces H 1 and BM O are deﬁned, and a rich theory is developed (see also [34] for more general measures on R n ).”
Moser iteration for (quasi)minimizers on metric spaces (2006, methodology): “For the formulation of the John–Nirenberg inequality and proofs of it valid in doubling metric spaces we refer to [9] and the appendix in Mateu– Mattila–Nicolau–Orobitg [33].”
Systems of dyadic cubes in a doubling metric space (2010, background): “ear how to prove something like this without the help of randomization. In more classical set-ups, similar conclusions could be reached with the help of strongly Euclidean devices like rotations; cf. [19], Theorem 2 and its proof. One immediate application of such a construction is the following. 6.”
H^1 and BMO for certain locally doubling metric measure spaces of finite measure (2008, background): “Finally, we recall that Hardy spaces and spaces of functions of bounded mean oscillation have recently been studied on various nondoubling metric measure spaces [14, 18, 19, 20].”
Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures (2002, background): “viding boundedness criteria in the spirit of the T(1) or T(b) theorems, were obtained as well (see [NTV3, MMNO , To3]).”
A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa (2009, background): “594, footnote] pointed out that John and Nirenberg’s proof “can be adapted to spaces of homogeneous type”, and explicit proofs can be found in [2], [14], [15].”
John–Nirenberg lemmas for a doubling measure (2009, background): “The lemma has previously been generalized to doubling metric measure spaces, for example, in [12], [2], [14], [15].”
A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition (2000, methodology): “Let us remark that other related decompositons with non doubling measures have been obtained in [NTV2] and [ MMNO ].”
A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure (2008, background): “Given a positive locally finite Borel measure μ on R, there exists a rotation such that all boundaries of rotated dyadic cubes have μ-measure zero (see [5] where they actually prove a stronger assertion when μ has no point masses, but our conclusion is obvious for a sum of point mass measures).”