摘要:

Letfbe a quasiconformal mapping of an open bounded setUinRnintoRn. Thenf′belongs toLp(U)for somep > nprovided thatfsatisfies (a)Uis a uniform domain andfUis a John domain or (b)fis quasisymmetric andUsatisfies a metric plumpness condition.

ISSN:0278-1077    

DOI:10.1080/17476938808814275

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

We show that the smallest constantc=c(mod(Q)) withfor allQsatisfies, where. A simple example establishes the lower bound. A new proof thatis bounded in terms of mod(Q) establishes the improved upper bound. We apply the method of proof to rings obtaining similar inequalities, one of which is sharp and provides a useful lower bound for the modulus of a ring.

ISSN:0278-1077    

DOI:10.1080/17476938808814276

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938808814277

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938808814278

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938808814279

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

This note presents a careful analysis of the level curves of the normalized univalent mapping of the unit disk onto the plane less a vertical slit and, in so doing, provides a negative answer to a question of Brannan on the level curves of univalent functions which are convex in one direction.

ISSN:0278-1077    

DOI:10.1080/17476938808814280

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938808814274

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor