To the theory of multiplicators of Fourier integrals for Banach-valued functions
Yazarlar (1)
Prof. Dr. Vagıf GULIYEV Kırşehir Ahi Evran Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (Uluslararası alan indekslerindeki dergilerde yayınlanan tam makale) | ||
| Dergi Adı | Proceedings of the Steklov Institute of Mathematics-Interperiodica Translation | ||
| Makale Dili | – | Basım Tarihi | 01-1996 |
| Cilt / Sayı / Sayfa | 214 / 0 / 157–174 | DOI | – |
| Makale Linki | https://scholar.google.com/scholar?cluster=12631165924300322364&hl=en&oi=scholarr | ||
| UAK Araştırma Alanları |
Matematiksel Analiz
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| Özet |
| The development of the new direction in the embedding theory, namely, the embedding of the spaces of abstract functions, was begun in the works of SL Sobolev and JL Lions. The further development belongs to VB Korotkov, A. Kh. Guliev, Yu. I. Gilderman, T. Muramatu, PI Lizorkin, VB Shakhmurov, AV Bukhvalov and others. Whereas for Banach-valued functions embedding theorems were obtained for a" nonoptimal exponent", in the cases of an" optimal exponent" embedding theorem were obtained (Bukhva-lov [1, 2]) only for isotropic spaces of UMD-valued functions. The main obstacle for the further development of the theory of embedding of anisotropic spaces of Banach-valued functions was the absence (even for UMD-valued functions) of the property of boundedness of anisotropic singular integral operators in L, and the theorem on Lp-multiplicators (the B-valued analog of Lizorkin's theorem). This obstacle was partially surmounted in the author's articles [3, 4](see also [5]) and in this article for the B spaces which are UMD-lattices. A brief exposition of a part of the results presented below is contained in the author's note [6]. The reader can find the exposition of various aspects of the theory of Lp-multiplicators of the Fourier integral in the books [7, 8], for instance. The corresponding theorems on multiplicators are formulated according to the type of the well-known Marcinkiewicz theorem and its versions. In [9, 10] and also in [11, 12] theorems on the multiplicators of Fourier integrals were obtained, which were used in studying isotropic as well as anisotropic spaces of differentiable functions of many variables. The aim of this article is the study … |
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