共查询到20条相似文献,搜索用时 250 毫秒
1.
Let
G ì \mathbb C G \subset {\mathbb C} be a finite region bounded by a Jordan curve L: = ?G L: = \partial G , let
W: = \textext[`(G)] \Omega : = {\text{ext}}\bar{G} (with respect to
[`(\mathbb C)] {\overline {\mathbb C}} ), $ \Delta : = \left\{ {z:\left| z \right| > 1} \right\} $ \Delta : = \left\{ {z:\left| z \right| > 1} \right\} , and let w = F(z) w = \Phi (z) be a univalent conformal mapping of Ω onto Δ normalized by $ \Phi \left( \infty \right) = \infty, \;\Phi '\left( \infty \right) > 0 $ \Phi \left( \infty \right) = \infty, \;\Phi '\left( \infty \right) > 0 . By A
p
(G); p > 0; we denote a class of functions f analytic in G and satisfying the condition
|| f ||App(G): = òG | f(z) |pdsz < ¥, \left\| f \right\|_{Ap}^p(G): = \int\limits_G {{{\left| {f(z)} \right|}^p}d{\sigma_z} < \infty, } 相似文献
2.
V. V. Zhuk 《Journal of Mathematical Sciences》2010,166(2):167-185
Let L
p
, 1 ≤ p< ∞, be the space of 2π-periodic functions f with the norm
|| f ||p = ( ò - pp | f |p )1 \mathord | / |
\vphantom 1 p p {\left\| f \right\|_p} = {\left( {\int\limits_{ - \pi }^\pi {{{\left| f \right|}^p}} } \right)^{{1 \mathord{\left/{\vphantom {1 p}} \right.} p}}} , and let C = L
∞ be the space of continuous 2π-periodic functions with the norm
|| f ||¥ = || f || = maxe ? \mathbbR | f(x) | {\left\| f \right\|_\infty } = \left\| f \right\| = \mathop {\max }\limits_{e \in \mathbb{R}} \left| {f(x)} \right| . Let CP be the subspace of C with a seminorm P invariant with respect to translation and such that
P(f) \leqslant M|| f || P(f) \leqslant M\left\| f \right\| for every f ∈ C. By ?k = 0¥ Ak (f) \sum\limits_{k = 0}^\infty {{A_k}} (f) denote the Fourier series of the function f, and let l = { lk }k = 0¥ \lambda = \left\{ {{\lambda_k}} \right\}_{k = 0}^\infty be a sequence of real numbers for which ?k = 0¥ lk Ak(f) \sum\limits_{k = 0}^\infty {{\lambda_k}} {A_k}(f) is the Fourier series of a certain function f
λ ∈ L
p
. The paper considers questions related to approximating the function f
λ by its Fourier sums S
n
(f
λ) on a point set and in the spaces L
p
and CP. Estimates for || fl - Sn( fl ) ||p {\left\| {{f_\lambda } - {S_n}\left( {{f_\lambda }} \right)} \right\|_p} and P(f
λ − S
n
(f
λ)) are obtained by using the structural characteristics (the best approximations and the moduli of continuity) of the functions
f and f
λ. As a rule, the essential part of deviation is estimated with the use of the structural characteristics of the function f.
Bibliography: 11 titles. 相似文献
3.
LetR
n be n-dimensional Euclidean space with n>-3. Demote by Ω
n
the unit sphere inR
n. ForfɛL(Ω
n
) we denote by σ
N
δ
its Cesàro means of order σ for spherical harmonic expansions. The special value
l = \tfracn - 22\lambda = \tfrac{{n - 2}}{2}
of σ is known as the critical one. For 0<σ≤λ, we set
p0 = \tfrac2ld+ lp_0 = \tfrac{{2\lambda }}{{\delta + \lambda }}
.
This paper proves that
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