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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2018, Volume 462, Issue 1, pp. 601 - 612
This paper is concerned with the study of harmonic measure on quasicircles and symmetric quasicircles. We investigate how the harmonic measure changes from one... 
Quasicircle | Harmonic measure | Quasisymmetric | Symmetric quasicircle | MATHEMATICS | MATHEMATICS, APPLIED | COUNTEREXAMPLE
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 10/2017, Volume 33, Issue 10, pp. 1321 - 1338
This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal... 
quasicircle | 30C62 | Mathematics, general | bi-Hölder | Mathematics | reduced extremal distance | 30C70 | Bi-Lipschitz | modulus | bi-Holder | MATHEMATICS | MATHEMATICS, APPLIED | QUASICIRCLES | Sewing | Mathematical analysis | Invariants
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 10/2013, Volume 45, Issue 5, pp. 911 - 920
The aim of this paper is to study the relations between the Hausdorff dimensions of k ‐quasilines and the theory of extremal quasiconformal mappings. We show... 
MATHEMATICS | CONFORMAL MAPPINGS | QUASICIRCLES
Journal Article
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, ISSN 1303-5010, 2019, Volume 48, Issue 1, pp. 87 - 101
The estimation of the modulus of algebraic polynomials on the boundary contour with weight function, having some singularities, with respect to the their... 
quasicircle | MATHEMATICS | INEQUALITIES | BEHAVIOR | algebraic polynomials | conformal mapping | STATISTICS & PROBABILITY | INTERFERENCE | BOUNDARY CONTOUR
Journal Article
Illinois Journal of Mathematics, ISSN 0019-2082, 2010, Volume 54, Issue 2, pp. 753 - 770
We characterize fractal chordarc curves in Euclidean space by the fact that they remain bilipschitz homogeneous under inversion. We illustrate this result by... 
MATHEMATICS | QUASICIRCLES
Journal Article
Filomat, ISSN 0354-5180, 2017, Volume 31, Issue 18, pp. 5647 - 5670
Journal Article
FILOMAT, ISSN 0354-5180, 2019, Volume 33, Issue 2, pp. 403 - 413
In this study, we give some estimates on the Nikolskii-type inequalities for complex algebraic polynomials in regions with piecewise smooth curves having... 
Bernstein inequalities | quasicircle | MATHEMATICS | MATHEMATICS, APPLIED | Nikol'skii inequalities | INEQUALITIES | conformal mapping | Polynomials
Journal Article
Kodai Mathematical Journal, ISSN 0386-5991, 2015, Volume 38, Issue 3, pp. 732 - 746
We consider quasiconformal deformations of C\Z. We give some criteria for infinitely often punctured planes to be quasiconformally equivalent to C\Z. In... 
and quasicircle | extremal distance | Quasiconformal mappings | Extremal distance | Quasicircle | quasicircle | MATHEMATICS | MAPS | SETS
Journal Article
Journal of Mathematical Sciences, ISSN 1072-3374, 10/2018, Volume 234, Issue 1, pp. 35 - 48
We have obtained the pointwise Bernstein–Walsh type estimation for algebraic polynomials in the unbounded regions with piecewise asymptotically conformal... 
quasicircle | Mathematics, general | conformal mapping | Mathematics | Algebraic polynomials | asymptotically conformal curve | DIAGRAMS | POLYNOMIALS | MATHEMATICAL SPACE | CONFORMAL MAPPING | MATHEMATICAL METHODS AND COMPUTING
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2018, Volume 463, Issue 1, pp. 19 - 39
In this paper we study integral estimates of derivatives of conformal mappings of the unit disc onto bounded domains Ω that satisfy the Ahlfors condition.... 
Conformal mappings | Quasiconformal mappings | Sobolev spaces | Elliptic equations | MATHEMATICS, APPLIED | SPACES | WEIGHTED SOBOLEV | MATHEMATICS | EIGENVALUES | HOMEOMORPHISMS | QUASICIRCLES | MAPPINGS | POINCARE INEQUALITIES
Journal Article
Filomat, ISSN 0354-5180, 2017, Volume 31, Issue 18, pp. 5647 - 5670
In this work, we investigate the order of the growth of the modulus of orthogonal polynomials over a contour and also arbitrary algebraic polynomials in... 
Algebraic polynomials | Cmooth curve | Conformal mapping | Quasicircle | Orthogonal polynomials | quasicircle | MATHEMATICS | cmooth curve | MATHEMATICS, APPLIED | algebraic polynomials | conformal mapping | BOUNDARY
Journal Article
Zhongshan Daxue Xuebao/Acta Scientiarum Natralium Universitatis Sunyatseni, ISSN 0529-6579, 07/2013, Volume 52, Issue 4, pp. 34 - 44
Journal Article
SIBERIAN MATHEMATICAL JOURNAL, ISSN 0037-4466, 01/2014, Volume 55, Issue 1, pp. 1 - 6
In 1937, Carath,odory proved that every injective mapping f: G -> f(G) aS, of a domain G aS, , taking circles to circles, is Mobius. The present article shows... 
quasicircle | MATHEMATICS | Mobius mapping | quasiconformal mapping | reverse isodiametric inequality
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 01/2014, Volume 55, Issue 1, pp. 1 - 6
In 1937, Caratheodory proved that every injective mapping f: G [right arrow] f(G) a C of a domain G a C , taking circles to circles, is Mobius. The present... 
Möbius mapping | quasicircle | quasiconformal mapping | reverse isodiametric inequality
Journal Article
Journal of Mathematical Sciences, ISSN 1072-3374, 2/2017, Volume 220, Issue 5, pp. 533 - 553
In the present work, we continue to study the growth of the orthogonal polynomials over a contour with a weight function in the weighted Lebesgue space, when... 
quasicircle | Orthogonal polynomials | algebraic polynomials | Mathematics, general | conformal mapping | Mathematics | smooth curve | Cytokinins | Analysis | Polynomials | Shape | Singularities | Weighting functions | Contours
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 08/2017, Volume 62, Issue 8, pp. 1117 - 1134
For a fixed integer , let be an m-connected region in the Riemann sphere whose complement is a union of m disjoint closed disks and let be quasisymmetric... 
quasicircle | 30G62 | conformal welding | Circle packing | 52C15 | 65N10 | 65N30 | quasisymmetric mapping | THEOREM | SEWING FUNCTIONS | MATHEMATICS | CIRCLE PACKINGS | CONVERGENCE | Welding
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 9/2016, Volume 57, Issue 5, pp. 747 - 753
We prove that every injective mapping of a domain $$D \subset \overline {{\mathbb{R}^n}} $$ D ⊂ ℝ n ¯ transforming spheres Σ ⊂ D to K-quasispheres (the images... 
quasiconformality coefficient | quasicircle | absolute cross-ratio | quasimöbius mapping | Mathematics, general | möbius mapping | Mathematics | quasiconformal mapping | separator | quasisphere | MATHEMATICS | MAPS | mobius mapping | quasimobius mapping | Automorphisms | Mapping
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 10/2017, Volume 11, Issue 7, pp. 1569 - 1586
In this work, we investigate the order of growth of the modulus of an arbitrary algebraic polynomials in the weighted Lebesgue space, where the contour and the... 
30C10 | Operator Theory | Primary 30A10 | Conformal mapping | Analysis | Mathematics, general | Mathematics | Algebraic polynomials | Orthonormal polynomials | Quasicircle | Secondary 41A17 | MATHEMATICS | MATHEMATICS, APPLIED | ORTHOGONAL POLYNOMIALS | COMPLEX-PLANE | BOUNDARY | Functions (mathematics) | Shape | Singularities | Mathematical analysis | Contours | Inequalities | Polynomials
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 1/2014, Volume 55, Issue 1, pp. 1 - 6
In 1937, Carathéodory proved that every injective mapping f: G → f(G) ⊂ $\bar C$ of a domain G ⊂ $\bar C$ , taking circles to circles, is Möbius. The present... 
Möbius mapping | quasicircle | Mathematics, general | Mathematics | quasiconformal mapping | reverse isodiametric inequality
Journal Article
STUDIA MATHEMATICA, ISSN 0039-3223, 2016, Volume 235, Issue 3, pp. 209 - 224
We prove that any weakly differentiable function with a square integrable gradient can be extended to the Caratheodory boundary of any simply connected planar... 
MATHEMATICS | SINGULARITIES | DIMENSION | QUASICIRCLES | SETS | QUASI-CONFORMAL MAPPINGS | POTENTIALS | Sobolev spaces | DOMAINS | conformal mappings | PRIME ENDS
Journal Article
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