Applications of Orlicz spaces

M.M. Rao, Z.D. Ren0824707303, 9780824707309, 9780585425146

Presents previously unpublished material on the fundamental principles and properties of Orlicz sequence and function spaces. Examines the sample path behavior of stochastic processes.

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Table of contents :
Front cover……Page 1
Pure and Applied Mathematics Editorial Board……Page 2
Pure and Applied Mathematics Series……Page 3
Title page……Page 9
Date-line……Page 10
Dedication……Page 11
Preface……Page 13
Contents……Page 17
1.1 $N$-functions and quantitative indices……Page 21
1.2 Some basic results on $L^Phi$-spaces……Page 33
1.3 Notes on Young functions and general measures……Page 48
1.4 Interpolation results on Orlicz spaces……Page 55
Bibliographical notes……Page 67
2.1 Introduction……Page 69
2.2 Lower bounds for $J(L^{(Phi)})$ and $c_{NJ}(L^Phi)$……Page 73
2.3 Upper bounds for $J(L^{(Phi)})$ and $J(L^Phi)$……Page 79
2.4 Sharp bounds for $c_{NJ}(L^{(Phi_s)})$ and $c_{NJ}(L^{Phi_s})$……Page 86
Bibliographical notes……Page 92
3.1 Introduction……Page 93
3.2 WCS and $N$-coefficients of Orlicz function spaces……Page 98
3.3 WCS coefficients of Orlicz sequence spaces……Page 110
3.4 More on Orlicz sequence spaces……Page 127
Bibliographical notes……Page 136
4.1 Introduction to Jung constants……Page 137
4.2 Lower bounds of $JC(L^{(Phi)})$ and $JC(L^Phi)$……Page 144
4.3 Bounds for $JC(L^{(Phi_s)})$ and $JC(L^{Phi_s})$……Page 155
4.4 Bounds for $JC(l^{(Phi)})$ and $JC(l^Phi)$……Page 158
Bibliographical notes……Page 165
5.1 Preliminaries……Page 167
5.2 Packing in Orlicz sequence spaces……Page 170
5.3 Packing in Orlicz function spaces……Page 187
5.4 Packing in reflexive Orlicz spaces……Page 195
Bibliographical notes……Page 203
6.1 Preliminaries on Fourier series……Page 204
6.2 Conjugate functions and Orlicz spaces……Page 210
6.3 Conjugate series and convergence in subsets of Orlicz spaces……Page 219
6.4 A Hausdorff-Young theorem for Orlicz spaces……Page 229
6.5 Fourier analysis on generalized Orlicz spaces……Page 247
Bibliographical notes……Page 254
7.1 Best predictions with convex loss……Page 256
7.2 When is a prediction operator linear?……Page 264
7.3 Nonlinear prediction for nonreflexive spaces……Page 269
7.4 Some extensions to vector valued functions……Page 280
Bibliographical notes……Page 291
8.1 Large deviations and Young functions……Page 293
8.2 Infinite dimensional extension and vector Orlicz spaces……Page 313
8.3 Regularity of stochastic functions and Orlicz spaces……Page 323
8.4 Martingales and Orlicz spaces……Page 333
Bibliographical notes……Page 345
9.1 Orlicz-Sobolev spaces for PDEs……Page 347
9.2 Removable singularities, PDE and Orlicz spaces……Page 365
9.3 Strong and weak type inequalities in Orlicz spaces……Page 376
9.4 Composition and Nemitsky operators in Orlicz spaces……Page 388
Bibliographical notes……Page 398
10.1 Beurling-Orlicz algebras……Page 400
10.2 Riesz angles of Orlicz spaces……Page 404
10.3 Embedding theorems for sequence spaces……Page 412
10.4 Differentiability properties of Orlicz spaces……Page 422
10.5 $L^{Phi^{-1}}$-spaces and applications……Page 431
Bibliographical notes……Page 456
References……Page 457
Notation……Page 477
Index……Page 481
Back cover……Page 485