The Möbius Invariance of Besov Spaces on the Unit Ball of C

نویسنده

  • KEHE ZHU
چکیده

It is well known that, for 1 ≤ p < ∞, the diagonal Besov space Bp of the open unit ball admits a norm or semi-norm ‖ ‖p such that ‖f ◦ φ‖p = ‖f‖p for all f in Bp and all automorphisms φ of the unit ball. We show here that the same result holds when 0 < p < 1.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On characterizations of hyperbolic harmonic Bloch and Besov spaces

‎We define hyperbolic harmonic $omega$-$alpha$-Bloch space‎ ‎$mathcal{B}_omega^alpha$ in the unit ball $mathbb{B}$ of ${mathbb R}^n$ and‎ ‎characterize it in terms of‎ ‎$$frac{omegabig((1-|x|^2)^{beta}(1-|y|^2)^{alpha-beta}big)|f(x)-f(y)|}{[x,y]^gamma|x-y|^{1-gamma}‎},$$ where $0leq gammaleq 1$‎. ‎Similar results are extended to‎ ‎little $omega$-$alpha$-Bloch and Besov spaces‎. ‎These obtained‎...

متن کامل

Harmonic Besov Spaces on the Unit Ball in R

We define and characterize the harmonic Besov space Bp, 1 ≤ p ≤ ∞, on the unit ball B in Rn. We prove that the Besov spaces Bp, 1 ≤ p ≤ ∞, are natural quotient spaces of certain Lp spaces. The dual of Bp, 1 ≤ p < ∞, can be identified with Bq , 1/p + 1/q = 1, and the dual of the little harmonic Bloch space B0 is B1.

متن کامل

Extended Cesáro Operators between Generalized Besov Spaces and Bloch Type Spaces in the Unit Ball

Let g be a holomorphic map of B, where B is the unit ball of C. Let 0 < p < +∞,−n − 1 < q < +∞, q > −1 and α > 0. This paper gives some necessary and sufficient conditions for the Extended Cesáro Operators induced by g to be bounded or compact between generalized Besov space B(p, q) and αBloch space B.

متن کامل

Möbius Invariant Hilbert Spaces of Holomorphic Functions in the Unit Ball of C"

We prove that there exists a unique Hubert space of holomorphic functions in the open unit ball of C" whose (semi-) inner product is invariant under Möbius transformations.

متن کامل

Weighted Lipschitz Continuity and Harmonic Bloch and Besov Spaces in the Real Unit Ball

The characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of Rn. Similar results are obtained for little Bloch and Besov spaces.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004