Abstract
A we mentioned in the Preface, Part II of this book deals with further types of function spaces which are more or less closely related to the spaces \(B_p^S\),q(R n ) and \(F_p^S\),q(R n ) from Chapter 2 and their counterparts on domains in Chapter 3. There are many possible modifications and we discuss a few of them. We restrict ourselves to formulations, comments, and occasionally to outlines of some basic ideas. As far as detailed proofs are concerned the reader is asked to consult the quoted references. In many cases the omitted proofs are more or less obvious modifications of corresponding proofs in Chapter 2. We shall give hints. This chapter deals with homogeneous spaces, which are very close to the "non-homogeneous" spaces from the second chapter. The periodic counterparts of these spaces are studied in Chapter 9. Chapters 7 and 8 deal with weighted counterparts. The necessary preparations for these two chapters will be given in Chapter 6. It deals with weighted spaces of entire analytic functions, and is a generalization and modification of the first chapter. Finally, in Chapter 10 we list very briefly further possibilities.
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Bergh, J.; Löfström, J. Interpolation Spaces. An Introduction. Berlin, Heidelberg, New York: Springer-Verlag 1976.
Calderón, A. P. Lebesgue spaces of functions and distributions. “Part. Diff. Equations”, Proc. Symp. Math. 4, Amer. Math. Soc., 1961, 33–49.
Calderón, A. P. Intermediate spaces and interpolation, the complex method. Studia Math. 24 (1964), 113–190.
Fefferman, C.; Stein, E. M.Hp spaces of several variables. Acta Math. 129 (1972), 137–193.
Peetre, J. New Thoughts on Besov Spaces. Duke Univ. Math. Series, Duke Univ., Durham, 1976.
Samko, S. G. The spaces \(L_{p,r}^{\alpha}(R^{n})\) and hyper-singular integrals. (Russian) Studia Math. 61 (1977), 193–230.
Samko, S. G. The description of the image of Iα(L p ) of Riesz potentials. (Russian) Izv. Akad. Nauk Armjan. SSR Ser. Mat. 12 (1977), 329–334.
Strichartz, R. S. Bounded mean oscillation and Sobolev spaces. Indiana Univ. Math. J. 29 (1980), 539–558.
Strichartz, R. S. Traces of BMO-Sobolev spaces. Proc. Amer. Math. Soc. 83, 3 (1981), 509–513.
Triebel, H. Theorems of Littlewood-Paley type for BMO and for anisotropic Hardy spaces. Proc. Intern. Conf. “Constructive Function Theory ‘77”, Sofia, 1980, 525–532.
Triebel, H. Characterizations of Besov-Hardy-Sobolev spaces via harmonic functions, temperatures and related means. J. Approximation Theory 35 (1982), 275–297.
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© 1983 Birkhäuser Basel
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Triebel, H. (1983). Homogeneous Function Spaces. In: Theory of Function Spaces. Modern Birkhäuser Classics. Springer, Basel. https://doi.org/10.1007/978-3-0346-0416-1_5
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DOI: https://doi.org/10.1007/978-3-0346-0416-1_5
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