Admissible limits of $M$-subharmonic functions.

Cima, Joseph A.; Stanton, Charles S.

doi:10.1307/mmj/1029003188

Cited by 11 publications

(5 citation statements)

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“…We remark that it has been observed in [3] that the invariant Green's function G is //-integrable with respect to the invariant measure dx(z) := (1 -\z\2)~n~x dv(z) on B for 1 < p < n/(n -1). This is a special case of the last theorem with a --n .…”

Section: Introductionmentioning

confidence: 84%

On the weighted $L^p$-integrability of nonnegative $\mathcal{M}$-superharmonic functions

Zhao¹

1992

Proc. Amer. Math. Soc.

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A weighted Z/-integrability of nonnegative .^-superharmonic functions in the unit ball of C is studied in this paper. Our result is analogous to an earlier result of Armitage (J. London Math. Soc. (2) 4 (1971), 363-373) concerning the ZZ-integrability of superharmonic functions for balls in R''. An example is given to show the sharpness of the result. Also, the weighted Lp-integrability of the invariant Green's function for the unit ball of C is obtained.

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Section: Introductionmentioning

confidence: 84%

On the weighted $L^p$-integrability of nonnegative $\mathcal{M}$-superharmonic functions

Zhao¹

1992

Proc. Amer. Math. Soc.

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“…The case of admissible limits, f--n and --1, was considered by J. Cima and C. S. Stanton in [2]. The purpose of this paper is to sharpen the above result by obtaining estimates on the exceptional set in terms of the 'non-isotropic' Hausdorff capacity on S.…”

Section: Theorem If F Is a Non-negative Measurable Function On B Satmentioning

confidence: 93%

“…In [2], J. Cima and C. S. Stanton showed that the potential of any measure # satisfying (1.1) has admissible limit zero in L q a.e. on S for any q < n/(n-1).…”

Section: E Convergence Of Potentialsmentioning

confidence: 99%

Non-isotropic hausdorff capacity of exceptional sets of invariant potentials

Stoll

1995

Potential Anal

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Abstract. In the paper we investigate tangential boundary limits of invariant Green potentials on the unit ball B in C", n i> 1. Let G(z, w) denote the Green function for the Laplace-Beltrami operator on B, and let )~ denote the invariant measure on B. If # is a non-negative measure, or f is a non-negative measurable function on B, G~ and G s denote the Green potential of # and f respectively. For {e S = OB, r >~ 1, and c>0, let ~,~(~)={ze B:lt-r n. Then for each z, 1 <~l:

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“…A slight modification of Example 1 of [2] shows that p > 1 is best possible for admissible limits, and consequently also for tangential limits.…”

Section: Sharpness Of Theoremmentioning

confidence: 99%

“…A. Cima and C . S. Stanton [2] and by M. Stoll [5, 61. In Section 2 we introduce the required notation and definitions and give the statement of the main theorems. In Section 3 we prove several lemmas that will be required for the proof of the main theorems which are given in Section 4.…”

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confidence: 99%

Boundary limits of pluri-green potentials in the unit ball of

Adzievski

1996

Complex Variables, Theory and Application: An International Jou

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Admissible limits of $M$-subharmonic functions.

Cited by 11 publications

References 0 publications

On the weighted $L^p$-integrability of nonnegative $\mathcal{M}$-superharmonic functions

On the weighted $L^p$-integrability of nonnegative $\mathcal{M}$-superharmonic functions

Non-isotropic hausdorff capacity of exceptional sets of invariant potentials

Boundary limits of pluri-green potentials in the unit ball of

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