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1.
A. V. Harutyunyan W. Lusky 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(3):128-135
Let U
n
be the unit polydisk in C
n
and S be the space of functions of regular variation. Let 1 ≤ p < ∞, ω = (ω
1, ..., ω
n
), ω
j
∈ S(1 ≤ j ≤ n) and f ∈ H(U
n
). The function f is said to be in holomorphic Besov space B
p
(ω) if
$
\left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}}
{{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }
$
\left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}}
{{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }
相似文献
2.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
3.
If p(z) is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then it is proved[5] that max |z|=1 |p′(z)| ≤ kn1n + kn m|z|=ax1 |p(z)|. In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type p(z) = cnzn + ∑n j=μ cn jzn j, 1 ≤μ≤ n. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros. 相似文献
4.
Let
be a nondecreasing sequence of positive numbers and let l
1,α be the space of real sequences
for which
. We associate every sequence ξ from l
1,α with a sequence
, where ϕ(·) is a permutation of the natural series such that
, j ∈ ℕ. If p is a bounded seminorm on l
1,α and
, then
5.
Rajendra Bhatia 《印度理论与应用数学杂志》2010,41(1):99-111
Lipschitz continuity of the matrix absolute value |A| = (A*A)1/2 is studied. Let A and B be invertible, and let M
1 = max(‖A‖, ‖B‖), M
2 = max(‖A
−1‖, ‖B
−1‖). Then it is shown that
|