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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.

Fractional Hardy inequalities and visibility of the boundary

100%

Ihnatsyeva L., Lehrbäck J., Tuominen H., Vähäkangas A.

Studia Mathematica

2014

tom 224

nr 1

47-80

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection with the boundedness of extension operators for fractional Sobolev spaces.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Studia Mathematica

2 Lehrbäck J.

2 Tuominen H.

1 Heikkinen T.

1 Ihnatsyeva L.

1 Nuutinen J.

1 Vähäkangas A.

1 2014

1 2013

Wyniki wyszukiwania

Fractional Maximal Functions in Metric Measure Spaces

Fractional Hardy inequalities and visibility of the boundary