Composition operators on Bergman spaces on Lavrentiev domains

References

• Duren , PL and Schuster , A . 2004 . “ Bergman Spaces ” . In Mathematical Surveys and Monographs , Providence, RI : AMS .
   Google Scholar
• Littlewood , JE . 1925 . On inequalities in the theory of functions. . Proceedings of the London Mathematical Society. Third Series , 23 : 481 – 519 .
   Google Scholar
• MacCluer , BD and Shapiro , JH . 1986 . Angular derivatives and compact composition operators on the Hardy and Bergman spaces. . Canadian Journal of Mathematics , 38 ( 4 ) : 878 – 906 .
   Web of Science ®Google Scholar
• Shapiro , JH and Smith , W . 2003 . Hardy spaces that supports no compact composition operators. . Journal of Functional Analysis , 205 : 62 – 89 .
   Web of Science ®Google Scholar
• Gallardo-Guiérrez , EA , González , M.J. and Nicolau , A . “ Composition operators on hardy spaces on Lavrentiev domains. ” . In Transactions of the American Mathematical Society (In press)
   Google Scholar
• Pommerenke , Ch. 1992 . Boundary Behaviour of Conformal Maps , Berlin : Springer-Verlag .
   Google Scholar
• Shapiro , JH . 1987 . The essential norm of a composition operator. . Annals of Mathematics , 125 : 375 – 404 .
   Web of Science ®Google Scholar
• Bruna , J and González , MJ . 1999 . L2 estimates on chord-arc curves. . Pacific Journal of Mathematics , 190 ( 2 ) : 225 – 233 .
   Web of Science ®Google Scholar
• Jerison , D and Kenig , C . 1982 . Hardy spaces, A∞, and singular integrals on chord-arc domains. . Mathematica Scandinavica , 50 : 221 – 247 .
   Web of Science ®Google Scholar
• Cowen , CC and MacCluer , BD . 1995 . Composition Operators on Spaces of Analytic Functions , Boca Raton, FL : CRC Press .
   Google Scholar
• Hedenmalm , H , Korenblum , B and Zhu , K . 2000 . “ Theory of Bergman spaces ” . In Graduate Text in Mathematics , Berlin : Springer-Verlag .
   Google Scholar
• Duren , PL . 1970 . Theory of Spaces , New York : Academic Press .
   Google Scholar
• Shapiro , JH . 1993 . Composition Operators and Classical Function Theory , Berlin : Springer-Verlag .
   Google Scholar