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Fractional Maximal Functions in Metric Measure Spaces

100%

Heikkinen T., Lehrbäck J., Nuutinen J., Tuominen H.

Analysis and Geometry in Metric Spaces

2013

tom 1

147-162

We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.

Angles between Curves in Metric Measure Spaces

88%

Han B.-X., Mondino A.

Analysis and Geometry in Metric Spaces

2017

tom 5

nr 1

47-68

The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay with optimal transportation and is particularly well suited for metric measure spaces satisfying the curvature-dimension condition. Indeed one of the main results is the validity of the cosine formula on RCD*(K, N) metric measure spaces. As a consequence, the new introduced notions are compatible with the corresponding classical ones for Riemannian manifolds, Ricci limit spaces and Alexandrov spaces.

The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces

75%

Lucia M., Puls M. J.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.

Ograniczanie wyników

3 Analysis and Geometry in Metric Spaces

1 Han B.-X.

1 Heikkinen T.

1 Lehrbäck J.

1 Lucia M.

1 Mondino A.

1 Nuutinen J.

1 Puls M. J.

1 Tuominen H.

1 2017

1 2015

1 2013

Wyniki wyszukiwania

Fractional Maximal Functions in Metric Measure Spaces

Angles between Curves in Metric Measure Spaces

The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces