TY - JOUR

T1 - On the coordinate functions of peano curves

AU - Makarov, B. M.

AU - Podkorytov, A. N.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - A construction of "nonsymmetric" plane Peano curves is described whose coordinate functions satisfy the Lipschitz conditions of orders a and 1 - α for some α. It is proved that these curves are metric isomorphisms between the interval [0,1] and the square [0,1]2. This fact is used to show that the graphs of their coordinate functions have the maximum possible Hausdorff dimension for a given smoothness.

AB - A construction of "nonsymmetric" plane Peano curves is described whose coordinate functions satisfy the Lipschitz conditions of orders a and 1 - α for some α. It is proved that these curves are metric isomorphisms between the interval [0,1] and the square [0,1]2. This fact is used to show that the graphs of their coordinate functions have the maximum possible Hausdorff dimension for a given smoothness.

KW - Hausdorff dimension

KW - Lipschitz condition

KW - Peano curve

UR - http://www.scopus.com/inward/record.url?scp=85010471371&partnerID=8YFLogxK

U2 - 10.1090/spmj/1441

DO - 10.1090/spmj/1441

M3 - Article

AN - SCOPUS:85010471371

VL - 28

SP - 115

EP - 125

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 1

ER -