Skip to main content Accessibility help
×
Home

Isometries of Weighted Bergman Spaces

  • Clinton J. Kolaski (a1)

Extract

In [2], [8] and [10], Forelli, Rudin and Schneider described the isometries of the Hp spaces over balls and polydiscs. Koranyi and Vagi [6] noted that their methods could be used to describe the isometries of the Hp spaces over bounded symmetric domains. Recently Kolaski [4] observed that the algebraic techniques used above and Rudin's theorem on equimeasurability extended to the Bergman spaces over bounded Runge domains. In this paper we use the same general argument to characterize the onto linear isometries of the weighted Bergman spaces over balls and polydiscs, (all isometries referred to are assumed to be linear).

2. Preliminaries. Horowitz [3] first defined the weighted Bergman space Ap,α (0 < p < ∞, 0 < α < ∞) to be the space of holomorphic functions f in the disc which satisfy

(1)

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Isometries of Weighted Bergman Spaces
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Isometries of Weighted Bergman Spaces
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Isometries of Weighted Bergman Spaces
      Available formats
      ×

Copyright

References

Hide All
1. Coif, R. R. man and Rochberg, R., Representation theorems for holomorphic and harmonic functions, to appear.
2. Forelli, F., A theorem on isometries and the application of it to the isometries of Hp﹛S) for 2 < p < ∞, Can. J. Math. 25 (1973), 284289.
3. Horowitz, C., Zeros of functions in the Bergman spaces, Duke Math. J. 41 (1974), 693710.
4. Kolaski, C., Isometries of Bergman spaces over bounded Runge domains, Can. J. Math. 33 (1981), 11571164.
5. Kolaski, C., Anew i00k ai a theorem of Forelli and Rudin, Indiana Univ. Math. J. 28 (1979), 495499.
6. Koranyi, A. and Vagi, S., Isometries of Hp spaces of bounded symmetric domains, Can. J. Math. 28 (1976), 334340.
7. Rudin, W., Function theory in polydiscs (Benjamin, 1969).
8. Rudin, W., Lp-isometries and equimeasurability, Indiana Univ. Math. J. 25 (1976), 215228.
9. Rudin, W., Function theory in the unit ball of Cn (Springer-Verlag, 1980).
10. Schneider, R., Iosmetries of Hv(Un), Can. J. Math. 25 (1973), 9295.
11. Taibleson, M. H. and Weiss, G., The molecular characterization of certain Hardy spaces, to appear.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Isometries of Weighted Bergman Spaces

  • Clinton J. Kolaski (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed