Characterisations of function spaces of generalised smoothness

Springer Science and Business Media LLC - Tập 185 Số 1 - Trang 1-62 - 2006
Walter Farkas1, Hans-Gerd Leopold2
1Swiss Banking Institute, University of Zurich, Plattenstrasse 14, CH-8032, Zurich, Switzerland
2Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 1–4, D-07740, Jena, Germany

Tóm tắt

Từ khóa


Tài liệu tham khảo

Adams, D.R., Hedberg, L.I.: Function spaces and potential theory. Berlin: Springer 1996

Bui, H.-Q., Paluszyński, M., Taibleson, M.: A maximal characterization of weighted Besov–Lipschitz and Triebel–Lizorkin spaces. Stud. Math. 119, 219–246 (1996)

Bui, H.-Q., Paluszyński, M., Taibleson, M.: Characterization of the Besov-Lipschitz and Triebel–Lizorkin spaces. The case q<1. J. Fourier Anal. Appl. 3, 837–846 (1997)

Burenkov, V.: Extension theorems for Sobolev spaces. Oper. Theory Adv. Appl. 109, 187–200 (1999)

Bricchi, M.: Tailored function spaces and related h-sets. PhD Thesis. University of Jena 2002

Cobos, F., Fernandez, D.L.: Hardy–Sobolev spaces and Besov spaces with a function parameter. Proc. Lund Conf. 1986, Lect. Notes Math. 1302, 158–170. Berlin: Springer 1986

Courrège, Ph.: Sur la forme intégro-différentielle des opérateurs de C K ∞ dans ℂ satisfaisant au principe du maximum. Exposé 2. Sém. Théorie du Potentiel, 1965/66, 38 pp

Edmunds, D.E., Haroske, D.: Spaces of Lipschitz type, embeddings and entropy numbers. Diss. Math. 380, 1–43 (1999)

Edmunds, D.E., Gurka, P., Opic, B.: On embeddings of logarithmic Bessel potential spaces. J. Funct. Anal. 146, 116–150 (1997)

Edmunds, D.E., Triebel, H.: Function spaces, entropy numbers, differential operators. Cambridge: Cambridge University Press 1996

Edmunds, D.E., Triebel, H.: Spectral theory for isotropic fractal drums. C. R. Acad. Sci. Paris 326, 1269–1274 (1998)

Edmunds, D.E., Triebel, H.: Eigenfrequencies of isotropic fractal drums. Oper. Theory Adv. Appl. 110, 81–102 (1999)

Farkas, W., Jacob, N., Schilling, R.L.: Feller semigroups, L p -sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols. Forum Math. 13, 59–90 (2001)

Farkas, W., Jacob, N., Schilling, R.L.: Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces. Diss. Math. 393, 1–62 (2001)

Farkas, W., Leopold, H.G.: Characterisations of function spaces of generalised smoothness. Jenaer Schriften zur Mathematik und Informatik 23, 1–56 (2001)

Fefferman, C., Stein, E.M.: Some maximal inequalities. Am. J. Math. 93, 107–115 (1971)

Frazier, M., Jawerth, B.: Decomposition of Besov spaces. Indiana Univ. Math. J. 34, 777–799 (1985)

Frazier, M., Jawerth, B.: A discrete transform and decomposition of distribution spaces. J. Funct. Anal. 93, 34–170 (1990)

Frazier, M., Jawerth, B.: Littlewood–Paley theory and the study of function spaces. CBMS Reg. Conf. Ser. Math. 79. Providence, RI: Am. Math. Soc. 1991

Fukushima, M.: Dirichlet spaces and strong Markov processes. Trans. Am. Math. Soc. 162, 185–224 (1971)

Goldman, M.L.: A description of the trace space for functions of a generalized Hölder class. Dokl. Akad. Nauk SSSR 231, 525–528 (1976)

Goldman, M.L.: A description of the traces of some function spaces Trudy Mat. Inst. Steklov 150, 99–127 (1979). English transl.: Proc. Steklov Inst. Math. 1981, no. 4 (150)

Goldman, M.L.: A method of coverings for describing general spaces of Besov type. Trudy Mat. Inst. Steklov 156, 47–81 (1980). English transl.: Proc. Steklov Inst. Math. 1983, no. 2 (156)

Goldman, M.L.: Imbedding theorems for anisotropic Nikol’skii–Besov spaces with moduli of continuity of general type. Trudy Mat. Inst. Steklov 170, 86–104 (1984). English transl.: Proc. Steklov Inst. Math. 1987, no. 1 (170)

Goldman, M.L.: Embedding of Nikol’skii–Besov spaces with moduli of continuity of general type in Lorentz spaces. Dokl. Akad. Nauk SSSR 277, 20–24 (1984)

Goldman, M.L.: On imbedding generalized Nikol’skii–Besov spaces in Lorentz spaces. Trudy Mat. Inst. Steklov 172, 128–139 (1985). English transl.: Proc. Steklov Inst. Math. 1987, no. 3 (172)

Goldman, M.L.: Embedding constructive and structural Lipschitz spaces in symmetric spaces. Trudy Mat. Inst. Steklov 173, 90–112 (1986). English transl.: Proc. Steklov Inst. Math. 1987, no. 4 (173)

Goldman, M.L.: Traces of functions with restrictions on the spectrum. Trudy Mat. Inst. Steklov 187, 69–77 (1989). English transl.: Proc. Steklov Inst. Math. 1990, no. 3 (187)

Goldman, M.L.: A criterion for the embedding of different metrics for isotropic Besov spaces with arbitrary moduli of continuity. Trudy Mat. Inst. Steklov 201, 186–218 (1992). English transl.: Proc. Steklov Inst. Math. 1994, no. 2 (201)

Jacob, N.: Pseudo-differential operators and Markov processes. Berlin: Akademie Verlag 1996

Jacob, N.: Characteristic functions and symbols in the theory of Feller processes. Potential Analysis 8, 61–68 (1998)

Jacob, N.: Pseudo-differential operators and Markov processes. Vol. 1: Fourier analysis and semigroups, World Scientific, Imperial College Press 2001

Jacob, N., Schilling, R.L.: Subordination in the sense of Bochner – An approach through pseudo-differential operators. Math. Nachr. 178, 199–231 (1996)

Kalyabin, G.A.: Characterization of spaces of generalized Liouville differentiation. Mat. Sb. Nov. Ser. 104, 42–48 (1977)

Kalyabin, G.A.: Imbedding theorems for generalized Besov and Liouville spaces. Dokl. Akad. Nauk SSSR 232, 1245–1248 (1977). English transl.: Soviet Math. Dokl. 1977, no 1 (18)

Kalyabin, G.A.: Trace spaces for generalized anisotropic Liouville classes. Izv. Akad. Nauk SSSR Ser. Mat. 42, 305–314 (1978). English transl.: Math. USSR Izv. 12 (1978)

Kalyabin, G.A.: A description of traces for anisotropic spaces of in classes of Triebel–Lizorkin type. Trudy Mat. Inst. Steklov 150, 160–173 (1979). English transl.: Proc. Steklov Inst. Math. 1981, no. 4 (150)

Kalyabin, G.A.: Description of functions in classes of Besov–Lizorkin–Triebel type. Trudy Mat. Inst. Steklov 156, 82–109 (1980). English transl.: Proc. Steklov Institut Math. 1983, no. 2 (156)

Kalyabin, G.A.: Criteria for multiplicativity and imbedding in C for spaces of Besov–Lizorkin–Triebel type. Mat. Zametki 30, 517–526 (1981). English transl.: in Math. Notes 1983, no. 30

Kalyabin, G.A.: Characterization of spaces of Besov–Lizorkin–Triebel type by means of generalized differences. Trudy Mat. Inst. Steklov 181, 95–116 (1988). English transl.: Proc. Steklov Inst. Math. 1989, no. 4 (181)

Kalyabin, G.A., Lizorkin, P.I.: Spaces of functions of generalized smoothness. Math. Nachr. 133, 7–32 (1987)

Kudryavtsev, L.D., Nikol’skii, S.M.: Spaces of differentiable functions of several variables and imbedding theorems. Analysis III, Spaces of differentiable functions, Encyclopadia of Math. Sciences 26, 4–140. Heidelberg: Springer 1990

Leopold, H.G.: Spaces of variable and generalised smoothness. Manuscript, Jena, 1990

Leopold, H.G.: Embeddings and entropy numbers in Besov spaces of generalized smoothness. in: Function Spaces: The fifth conference, Lecture Notes Pure Appl. Math. 213, 323–336. Hudzik, H., Skrzypczak, L.(eds.). Marcel Dekker 2000

Merucci, C.: Applications of interpolation with a function parameter to Lorentz, Sobolev and Besov spaces. Proc. Lund Conf. 1983. Lect. Notes Math. 1070, 183–201. Berlin: Springer

Moura, S.: Some properties of the spaces F(s,Ψ) pq (ℝ n ) and B(s,Ψ) pq (ℝ n ). Preprint 99–09, Univ. Coimbra 1999

Moura, S.: Function spaces of generalised smoothness. Diss. Math. 398, 1–87 (2001)

Netrusov, Y.V.: Embedding theorems for traces of Besov spaces and Lizorkin-Triebel spaces. Dokl. Akad. Nauk SSSR 298, 1326–1330 (1988). English transl.: Soviet Math. Dokl. 1988, no. 1 (37)

Netrusov, Y.V.: Metric estimates of the capacities of sets in Besov spaces. Trudy Mat. Inst. Steklov 190, 159–185 (1989). English transl.: Proc. Steklov Inst. Math. 1992, no. 1 (190)

Opic, B., Trebels, W.: Bessel potentials with logarithmic components and Sobolev-type embeddings. Anal. Math. 26, 299–319 (2000)

Peetre, J.: On spaces of Triebel Lizorkin type. Ark. Mat. 13, 123–130 (1975)

Rychkov, V.: On a theorem of Bui, Paluszyński, and Taibleson. Trudy Mat. Inst. Steklov 227, 286–298 (1999). English transl.: Proc. Steklov Inst. Math. 227, 280–292 (1999)

Schilling, R.L.: Zum Pfadverhalten von Markovschen Prozessen, die mit Lévy Prozessen vergleichbar sind. Dissertation Universität Erlangen–Nürnberg, Erlangen 1994

Schilling, R.L.: Subordination in the sense of Bochner and a related functional calculus. J. Aust. Math. Soc. 64, 368–396 (1998)

Schilling, R.L.: Conservativeness of semigroups generated by pseudo-differential operators. Potential Anal. 9, 91–104 (1998)

Schmeisser, H.J., Triebel, H.: Topics in Fourier analysis and function spaces. Leipzig: Geest & Portig 1987

Stein, E.M., Weiss, G.: Introduction to Fourier analysis on euclidean spaces. Princeton, NJ: Princeton Univ. Press 1971

Strömberg, J.O., Torchinsky, A.: Weighted Hardy spaces. Lect. Notes Math. 1381. Berlin: Springer 1989

Triebel, H.: Fourier analysis and function spaces. Teubner-Texte Math. 7. Leipzig: Teubner 1977

Triebel, H.: Interpolation theory, function spaces, differential operators. Amsterdam: North Holland 1978

Triebel, H.: Theory of function spaces. Leipzig: Geest & Portig and Basel: Birkhäuser 1983

Triebel, H.: Theory of function spaces. Russian ed. Moscow: Mir 1986

Triebel, H.: Characterizations of Besov–Hardy–Sobolev spaces: a unified approach. J. Approximation Theory 52, 162–203 (1988)

Triebel, H.: Theory of function spaces II. Basel: Birkhäuser 1992

Triebel, H.: Fractals and spectra, related to Fourier Analysis and Function Spaces. Basel: Birkhäuser 1997

Triebel, H.: The structure of functions. Basel: Birkhäuser 2001

Triebel, H., Winkelvoß, H.: A Fourier analytical characterization of the Hausdorff dimension of a closed set and of related Lebesgue spaces. Stud. Math. 121, 149–166 (1996)