Artículo
Hölder coverings of sets of small dimension
Fecha de publicación:
24/06/2019
Editorial:
European Mathematical Society
Revista:
Journal of Fractal Geometry
ISSN:
2308-1309
e-ISSN:
2308-1317
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We show that a set of small box counting dimension can be covered by a H¨older graph from all but a small set of directions, and give sharp bounds for the dimension of the exceptional set, improving a result of B. Hunt and V. Kaloshin. We observe that, as a consequence, H¨older graphs can have positive doubling measure, answering a question of T. Ojala and T. Rajala. We also give remarks on H¨older coverings in polar coordinates and, on the other hand, prove that a Homogenous set of small box counting dimension can be covered by a Lipschitz graph from all but a small set of directions.
Palabras clave:
BOX DIMENSION
,
HOLDER GRAPH
,
THIN SETS
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Articulos(SEDE CENTRAL)
Articulos de SEDE CENTRAL
Articulos de SEDE CENTRAL
Citación
Rossi, Eino Vihtori; Shmerkin, Pablo Sebastian; Hölder coverings of sets of small dimension; European Mathematical Society; Journal of Fractal Geometry; 6; 3; 24-6-2019; 285-299
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