Folland G.B., Stein E.M. — Hardy Spaces on Homogeneous Groups :: Электронная библиотека попечительского совета мехмата МГУ

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Folland G.B., Stein E.M. — Hardy Spaces on Homogeneous Groups

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Название: Hardy Spaces on Homogeneous Groups

Авторы: Folland G.B., Stein E.M.

Аннотация:

The object of this monograph Is to give an exposition of the real-variable theory of Hardy spaces (H^p spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in IR^n of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development it seems to us that a systematic exposition of some of the main parts of this theory is now desirable. There are, however, good reasons why in addition the theory should be recast in the more general setting where the underlying IR^n is replaced by a homogeneous group. The justification for this wider scope, both in terms of the structure of the theory and its applications, will be described in more detail below.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 284

Добавлена в каталог: 05.12.2009

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Предметный указатель

(p,q,a)—atom      71
Admissible      71
Area integral      217
Associated (to a ball)      72
atom      71
Atomic decomposition      76
Atomic Hardy space      75
Ball      8
Calderon — Zygmund decomposition      83
Campanato space      142
Campbell — Hausdorff formula      2
Chebyshev's inequality      13
Commutative approximate identity      116
Constants: $d_{j}$       7
Constants: $N_{p}$       72
Constants: $\beta$       29
Constants: $\gamma$       12
Constants: $\mathcall{Q}$       10
Constants: $\nu$       31
Constants: $\overline{d}$       7
Constants: n      7
Convolution      15
Degree (of Calderon — Zygmund decomposition)      83
Derivatives and multiindices: $X^{I}$       21
Derivatives and multiindices: $X_{j}$       7
Derivatives and multiindices: $Y^{I}$       21
Derivatives and multiindices: $Y_{j}$       20
Derivatives and multiindices: d(I)      21
Derivatives and multiindices: |I|      21
Dilations      4
Dilations: $\delta_{r}$       4
Dilations: rx      6
Dilations: x/r      6
Distribution function      13
Graded      5
Grand maximal function      70
Hardy space      75
Hardy — Littlewood maximal function      67
Heat kernel      58
Heat kernel: $H_{t}$       57
Heat kernel: h      56
Heat semigroup      58
Height (of Calderon — Zygmund decomposition)      83
Heisenberg group      8
Homogeneous degree (of differential operator)      21
Homogeneous degree (of polynomial)      22
Homogeneous differential operator      10
Homogeneous dimension      10
Homogeneous distribution      10
Homogeneous function      10
Homogeneous group      5
Homogeneous norm      8
Isotropic degree      22
Kernel of type ( $\alpha$ ,r) ( $\alpha$ >0)      184
Kernel of type (0,r)      185
Littlewood — Paley function      217
Lover central series      2
Lusin and Littlewood — Paley functions: $g_{j}$       241
Lusin and Littlewood — Paley functions: $g_{\Phi}$       218
Lusin and Littlewood — Paley functions: $G_{\Phi}^{\lambda}$       218
Lusin and Littlewood — Paley functions: $S_{j}$       241
Lusin and Littlewood — Paley functions: $S_{\Phi}$       217
Lusin and Littlewood — Paley functions: $S_{\Phi}^{\alpha}$       217
Lusin function      217
Maximal functions: $M_{(N)}$       70
Maximal functions: $M_{(N)}^{0}$       70
Maximal functions: $M_{HL}$       67
Maximal functions: $M_{\Phi}$       62
Maximal functions: $M_{\Phi}^{0}$       62
Maximal functions: $T_{\Phi}^{\lambda}$       115
Nilpotent      2
Nonincreasing rearrangement      13

Nontangential maximal function      62
Norms, quasinorms, seminorms: $[\ ]_{p}$       13
Norms, quasinorms, seminorms: $\mu^{p}_{q,a}$       141
Norms, quasinorms, seminorms: $\nu^{\alpha}_{N}$       157
Norms, quasinorms, seminorms: $\nu^{\alpha}_{q,a}$       142
Norms, quasinorms, seminorms: $\rho^{p}$       76
Norms, quasinorms, seminorms: $\rho^{p}_{q,a}$       76
Norms, quasinorms, seminorms: $\|\ \|_{(I,j)}$       280
Norms, quasinorms, seminorms: $\|\ \|_{(N)}$       35
Norms, quasinorms, seminorms: $\|\ \|_{BMO}$       146
Norms, quasinorms, seminorms: $\|\ \|_{p}$       13
Norms, quasinorms, seminorms: $\|\ \|_{_{C}(s)}$       212
Norms, quasinorms, seminorms: $|\ \hat{|_{\alpha}}$       158
Norms, quasinorms, seminorms: $|\ |_{\alpha}$       158
Norms, quasinorms, seminorms: | |      8
Other operations on functions: $m_{B}u$       146
Other operations on functions: $u^{\#}$       149
Other operations on functions: $\lambda_{f}$       13
Other operations on functions: $\Phi_{t}$       18
Other operations on functions: f*      13
Other operations on functions: f*g      15
P-admissible      71
Poisson kernel      254
Poisson — Szegoe kernel      254
Polynomial      22
Polyradial      139
Positive operator      129
Radial maximal function      62
Rockland operator, (R-operator)      129
Schwartz class      35
Sets: $E^{c}$       1
Sets: $\Delta$       24
Sets: $\mathbb{C}$       1
Sets: $\mathds{N}$       1
Sets: $\mathds{R}$       1
Sets: $\mathds{Z}$       1
Sets: $\overline{E}$       1
Sets: B(r,x)      8
Sets: |E|      10
Sharp function      149
Spaces of functions and distributions: $C(\Omega)$       12
Spaces of functions and distributions: $C^{(k)}$       12
Spaces of functions and distributions: $C^{k}$       33
Spaces of functions and distributions: $C^{\alpha}_{N}$       157
Spaces of functions and distributions: $C^{\alpha}_{q,a}$       142
Spaces of functions and distributions: $C^{\infty}$       12
Spaces of functions and distributions: $C^{\infty}_{0}$       12
Spaces of functions and distributions: $C_{0}$       12
Spaces of functions and distributions: $C_{c}$       12
Spaces of functions and distributions: $H^{p}$       75
Spaces of functions and distributions: $H^{p}_{q,a}$       75
Spaces of functions and distributions: $L^{p}$       12
Spaces of functions and distributions: $\Gamma^{hom}_{\alpha}$       158
Spaces of functions and distributions: $\hat{\Gamma}^{hom}_{\alpha}$       158
Spaces of functions and distributions: $\hat{\mathcal{N}}_{\alpha}$       158
Spaces of functions and distributions: $\mathcal{N}_{\alpha}$       158
Spaces of functions and distributions: $\mathcal{P}_{a}$       23
Spaces of functions and distributions: $\mathcal{P}_{N}^{iso}$       23
Spaces of functions and distributions: $\mathcal{R'}$       256
Spaces of functions and distributions: $\mathcal{R}$       253
Spaces of functions and distributions: $\mathcal{S'}$       35
Spaces of functions and distributions: $\mathcal{S}$       35
Spaces of functions and distributions: BMO      146
Spaces of functions and distributions: weak $L^{p}$       13
STEP      2
stratified      5
Sub-Laplacian      55
Sub-Laplacian: L      55
Tangential maximal function      115
Tempered distribution      38
Vanish weakly at infinity      50
Weak type      13
Young's inequality      16

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