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Bergh J., Löfström J. — Interpolation Spaces: An Introduction
Bergh J., Löfström J. — Interpolation Spaces: An Introduction



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Название: Interpolation Spaces: An Introduction

Авторы: Bergh J., Löfström J.

Аннотация:

The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J-L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works-of others (with the exception of a few minor contributions of our own).


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1976

Количество страниц: 207

Добавлена в каталог: 27.04.2010

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Предметный указатель
$A_0+A_1$      24
$B_{pq}^s$, $H_p^s$, $\|\cdot\|_{pq}^s$, $\|\cdot\|_p^s$      141
$C^{\theta}$, $C^{\theta}(\bar A)$, $\bar A^{[\theta]}$      89
$c_0^s$, $c_0^s(A)$, $\dot c_0^s$, $\dot c_0^s(A)$      121
$C_{\theta}$, $C_{\theta}(\bar A)$, $\bar A_{[\theta]}$      88
$D^{\alpha}$      131
$E(t,a)$, $E(t,a;\bar A)$      174
$E_{\alpha q(\bar A)}$, $\|\cdot\|_{\alpha,q,E}$      177
$H_p$      18 168
$J(t,a;\bar A)$, $J(t,a)$      (31) 42
$J^s$, $I^s$      139
$K(t,a;\bar A)$, $K(t,a)$      (31) 38
$K_p(t)$, $K_p(t,a)$      75 115
$L_0$      62
$L_p$      13
$L_p$, $L_p(U)$, $L_p(d\mu)$, $L_p(U,d\mu)$      1
$L_p(A)$, $L_p(U,d\mu;A)$      107
$L_p(w)$      11
$L_p^*(A)$      70
$l_q^s$, $l_q^s(A)$, $\dot{l}_q^s$, $\dot{l}_q^s(A)$      121
$L_\infty^0(A)$      107
$L_{pr}$      8
$m(\sigma,f)$      6
$M_p$      132
$M_p(H_0,H_1)$      134
$S(p_0,\xi_0,A_0;p_1,\xi_1,A_1)$      85
$S(\bar A,\bar p,\theta)$, $\underline{S}(\bar A,\bar p,\theta)$      70
$T^m(\bar A,\bar p,\theta)$      72
$T_0^m(p_0,\alpha_0,A_0;p_1,\alpha_1,A_1)$      86
$T_j^m(\bar A,\bar p,\bar{\eta})$      79
$V^m(\bar A,\bar p,\theta)$      72
$V_m(p_0,\alpha_0,A_0;p_1,\alpha_1,A_1)$      86
$W_p^N$      153
$\bar A$      25
$\bar A_{\theta,q;J}$, $J_{\theta,q}(\bar A)$, $\|\cdot\|_{\theta,q;J}$      42
$\bar A_{\theta,q;K}$, $K_{\theta,q}(\bar A)$, $\|\cdot\|_{\theta,q,K}$      40
$\bar A_{\theta,q}$, $\|\cdot\|_{\theta,q}$      46
$\Delta(\bar A)$, $\Sigma(\bar A)$      26
$\Delta_{\gamma}^m$      144
$\dot{B}_{pq}^s$, $\dot{H}_p^s$, $\|\cdot\dot{\|}_{pq}^s$, $\|\cdot\dot{\|}_p^s$      147
$\lambda^{\theta,q}$      41
$\mathscr{B}$      24
$\mathscr{C}$      22
$\mathscr{C}_1$      25
$\mathscr{C}_K(\theta;\bar A)$, $\mathscr{C}_J(\theta;\bar A)$, $\mathscr{C}(\theta;\bar A)$      48
$\mathscr{E}_p$      180
$\mathscr{F}(\bar A)$, $\mathscr{F}$      87
$\mathscr{F}f$, $\hat f$      5
$\mathscr{F}_0(\bar A)$      91
$\mathscr{G}(\bar A)$, $\mathscr{G}$      88
$\mathscr{N}$      23
$\mathscr{S}$, $\mathscr{S}'$      131 132
$\mathscr{S}(H)$, $\mathscr{S}'(H)$      134
$\omega_p^m(t;f)$      143
$\Phi_{\theta,q}$      39
$\tilde V^m(\bar A,\bar p,\bar{\eta})$      74
$\underline{S}(p_0,\xi_0,A_0;p_1,\xi_1,A_1)$      86
$\|T\|_{A,B}$      23 26
$\|\cdot\dot{\|}_{pq}^s$      146
$\|\cdot\dot{\|}_{p}^s$      147
$\|\cdot\|_{pq}^s$, $\|\cdot\|_{p}^s$      140
Approximation space      177
Aronszajn — Gagliardo theorem      29
Bernstein's inequality      (12) 180
Besov space      141 146
Bessel potential      139
Bounded interpolation functor      28
c-norm      59
c-triangle inequality      59
Calderon's interpolation theorem      114
Compatible spaces, couples      24 63
Decreasing rearrangement      7
Difference schemes      183
Duality theorem for the complex method      98
Duality theorem for the real method      54
Embedding theorem      153
Entire function      180
Equivalence theorem for the complex method      93
Equivalence theorem for the real method      44 65
Espaces de moyennes      70
Espaces de traces      72
Exact interpolation functor      28
Exact interpolation space      27
F*      7
Fourier multiplier      132
Fourier transform      5 131
Function norm      78
Fundamental lemma of interpolation theory      45
Gagliardo completition      37
Gagliardo diagram      39
Gagliardo set      175
Hardy class, space      18 170
Hardy's inequality      16
Hausdorff — Young's inequality      6
Hilbert transform      15
Holmstedt's formula (theorem 3.6.1)      52
Homogeneous Besov space      146
Inequality of Bernstein      (12) 180
Inequality of Hardy      16
Inequality of Hausdorff — Young      6
Inequality of Jackson      (12) 180
Inequality of Young      6
Infinitesimal generator      157
Intermediate space      26
Intermediate space of class $\mathscr{C}(\theta;\bar A)$      48
Interpolation function      116
Interpolation functor (method)      28
Interpolation of compact operators      56 85
Interpolation of locally convex spaces      83
Interpolation of multilinear mappings      (9) 76 96
Interpolation of non-linear mappings      36 78
Interpolation of semi-normed spaces      83
Interpolation space      27
Interpolation theorem of Calderon      114
Interpolation theorem of Marcinkiewicz      9 113
Interpolation theorem of Riesz — Thorin      2 107
Interpolation theorem of Stein — Weiss      115
Jackson's inequality      (12) 180
K-monotonic spaces      84
Lebesgue space      1
Lorentz space      8
Orlicz spaces      128
p-nuclear operators      182
Potentials      139
Power theorem      68
Quasi-concave functions      84 117
Quasi-linearizable couples      77
Quasi-norm      (7) 59
Quasi-normed Abelian groups      59
Quasi-normed Abelian semi-groups      80
Quasi-normed vector space      7
Real interpolation method      46
Reiteration theorem for the complex method      101
Reiteration theorem for the real method      50 67
retract      (81) 150
Riesz potential      139
Riesz — Thorin's interpolation theorem      2 107
Scales of Banach spaces      82
Semi-groups of operators      157
Sobolev space      141 153
Spline functions      193
Stability theorem      see equivalence theorem
Stein — Weiss interpolation theorem      115
Three line theorem      4
Trace theorem      155
Uniform interpolation functor      28
Uniform interpolation space      27
Weak reiteration theorem      35
Young's inequality      6
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