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Boundary behavior of subharmonic functions in nontangential accessible domains

100%
Zhao S.
Studia Mathematica
|
1994
|
tom 108
|
nr 1
25-48
EN
The following results concerning boundary behavior of subharmonic functions in the unit ball of $ℝ^n$ are generalized to nontangential accessible domains in the sense of Jerison and Kenig [7]: (i) The classical theorem of Littlewood on the radial limits. (ii) Ziomek's theorem on the $L^p$-nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.
2
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On weighted inequalities for operators of potential type

100%
Zhao S.
Colloquium Mathematicum
|
1996
|
tom 69
|
nr 1
95-115
EN
In this paper, we discuss a class of weighted inequalities for operators of potential type on homogeneous spaces. We give sufficient conditions for the weak and strong type weighted inequalities sup_{λ>0} λ|{x ∈ X : |T(fdσ)(x)|>λ }|_{ω}^{1/q} ≤ C (∫_{X} |f|^{p}dσ)^{1/p} and (∫_{X} |T(fdσ)|^{q}dω )^{1/q} ≤ C (∫_X |f|^{p}dσ )^{1/p} in the cases of 0 < q < p ≤ ∞ and 1 ≤ q < p < ∞, respectively, where T is an operator of potential type, and ω and σ are Borel measures on the homogeneous space X. We show that under certain restrictions on the measures those sufficient conditions are also necessary. A consequence is given for the fractional integrals in Euclidean spaces.
3
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Weak type estimates for operators of potential type

63%
Wheeden R. L., Zhao S.
Studia Mathematica
|
1996
|
tom 119
|
nr 2
149-160
EN
We derive two-weight weak type estimates for operators of potential type in homogeneous spaces. The conditions imposed on the weights are testing conditions of the kind first studied by E. T. Sawyer [4]. We also give some applications to strong type estimates as well as to operators on half-spaces.
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