Dissertationes mathematicae. 489: A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces / Yiyu Liang, Dachun Yang, Wen Yuan, Yoshihiro Sawano, Tino Ullrich; Institute of Mathematics, Polish Academy of Sciences. - Warszawa: Instytut matematyczny PAN, 2012. - 114 p. - Ref.: p.110-114. - ISSN 0012-3862  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

1 Introduction ................................................. 6 2 Fundamental settings and inequalities ....................... 13 2.1 Basic assumptions ...................................... 13 2.2 Inequalities ........................................... 17 3 Besov-type and Triebel-Lizorkin-type spaces ................. 21 3.1 Definitions ............................................ 21 3.2 Fundamental properties ................................. 25 4 Atomic decompositions and wavelets .......................... 32 4.1 Atoms and molecules .................................... 32 4.2 Proof of Theorem 4.5 ................................... 34 4.3 The regular case ....................................... 37 4.4 Biorthogonal wavelet decompositions .................... 40 5 Pointwise multipliers and function spaces on domains ........ 45 5.1 Pointwise multipliers .................................. 45 5.2 Function spaces on domains ............................. 46 6 Boundedness of operators .................................... 51 6.1 Boundedness of Fourier multipliers ..................... 51 6.2 Boundedness of pseudo-differential operators ........... 55 7 Embeddings .................................................. 59 7.1 Embedding into C(n) ................................... 59 7.2 Function spaces AwτL,q,α(n) for τ large ................ 59 8 Characterizations via differences and oscillations .......... 62 8.1 Characterization by differences ........................ 62 8.2 Characterization by oscillations ....................... 68 9 Isomorphisms between spaces ................................. 72 9.1 The role of the new parameter a ........................ 72 9.2 Identification of the space (n) ...................... 77 9.3 F-spaces and ε-spaces .................................. 78 10 Homogeneous spaces .......................................... 83 10.1 Homogeneous Besov-type and Triebel-Lizorkin-type spaces ................................................. 84 10.2 Characterizations ...................................... 86 10.3 Atomic decompositions .................................. 87 10.4 Boundedness of operators ............................... 89 10.5 Function spaces AwτL,q,α(n) for τ large ................ 92 10.6 Characterizations via differences and oscillations ..... 93 11 Applications and examples ................................... 95 11.1 Weighted Lebesgue spaces ............................... 95 11.2 Morrey spaces .......................................... 95 11.3 Orlicz spaces .......................................... 98 11.4 Herz spaces ........................................... 101 11.5 Variable exponent Lebesgue spaces ..................... 101 11.6 Amalgam spaces ........................................ 103 11.7 Multiplier spaces ..................................... 103 11.8 Ḃσ(n) spaces ......................................... 105 11.9 Generalized Campanato spaces .......................... 107 References .................................................... 110