Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Strong type estimate and Carleson measures
for Lipschitz spaces

Author: Zhijian Wu
Journal: Proc. Amer. Math. Soc. 127 (1999), 3243-3249
MSC (1991): Primary 31C15, 42B25
Published electronically: May 4, 1999
MathSciNet review: 1637452
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We establish a capacitary strong type estimate for Lipschitz space ${\mathcal{\Lambda }_{\alpha }^{\!p,q}}$ and characterize the related Carleson measures.

References [Enhancements On Off] (What's this?)

  • [A] D. R. Adams, On the existence of capacitary strong type estimates in $\mathbb{R}^{n}$, Arkiv Math 14 (1976), 125-140. MR 54:5822
  • [H] K. Hansson, Imbedding theorems of Sobolev type in potential theory, Math. Scand. 45 (1979), 77-102. MR 81j:31007
  • [KS] R. Kerman and E. Sawyer, Carleson measures and multipliers of Dirichlet spaces, Trans. Amer. Math. Soc. 309 (1988), 87-98. MR 89i:30044
  • [MS] V. G. Ma\'{z}ya and T. O. Shaposhnikova, Theory of Multipliers in Spaces of Differentiable Functions, Pitman Advanced Publishing Program, Boston and London. MR 87j:46074
  • [RW] R. Rochberg and Z. Wu, A new characterization of Dirichlet type spaces and its applications, Illinois J. Math. (1) 37 (1993), 101-122. MR 93j:30039
  • [S] D. Stegenga, Multipliers of the Dirichlet space, Illinois J. Math. 24 (1980), 113-139. MR 81a:30027
  • [St] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton Univ., 1970. MR 44:7280
  • [W1] Z. Wu, The predual and second predual of $W_{\!\alpha }$, J. Funct. Anal. (2) 116 (1993), 314-334. MR 94g:46033
  • [W2] -, A class of bilinear forms on Dirichlet type spaces, J. London Math. Soc. (2) 54 (1996), 498-514. MR 97h:46039
  • [W3] -, Clifford analysis and commutators on the Besov spaces, J. Funct. Anal., to appear.
  • [Z] W. P. Ziemer, Weakly Differentiable Functions, Springer-Verlag, New York, 1989. MR 91e:46046

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 31C15, 42B25

Retrieve articles in all journals with MSC (1991): 31C15, 42B25

Additional Information

Zhijian Wu
Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487

Keywords: Lipschitz spaces, capacity, Carleson measures, strong estimate
Received by editor(s): January 25, 1998
Published electronically: May 4, 1999
Additional Notes: The author’s research was supported by National Science Foundation DMS 9622890
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society