Abstract
The article is a survey of results concerning radial subspaces of Besov and Lizorkin-Triebel spaces.
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References
B. Berestycki and P.L. Lions, Existence of a ground state in nonlinear equations of the type Klein-Gordon. In: Variational Inequalities and complementary theory and applications, Wiley, New York 1979.
G.L. Bredon, Introduction to compact transformation groups, Academic Press, New York-London, 1972.
S. Coleman, V. Glazer, and A. Martin, Action minima among solutions to a class of euclidean scalar field equations, Comm. in Math. Physics 58 (1978), 211–221.
Y. Ebihara and T.P. Schonbek, On the (non) compactness of the radial Sobolev spaces, Hiroshima Math. J. 16 (1986), 665–669.
D.E. Edmunds, R.M. Edmunds and H. Triebel, Entropy numbers of embeddings of fractional Besov-Sobolev spaces in Orlicz spaces, J. London Math. Soc. 35 (1987), 121–134.
D.E. Edmunds and H. Triebel, Function spaces, entropy numbers and differential operators. Cambridge Univ. Press, Cambridge 1996.
D.E. Edmunds and H. Triebel, Sharp Sobolev embeddings and related Hardy inequalities: The critical case, Math. Nachr. 207 (1999), 79–92.
J. Epperson and M. Frazier, An almost orthogonal radial wavelet expansion for radial distributions, J. Fourier Analysis Appl. 1 (1995), 311–353.
M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, J. Funct. Anal. 93 (1990), 34–170.
D. Haroske, Embeddings of some weighted function spaces on IF V: entropy and approximation numbers, An. Univ. Craiova, Ser. Mat. Inform 26 (1997), 1–44.
D. Haroske, H. Triebel, Entropy numbers in weighted function spaces and eigenvalues distribution of some degenerated pseudodifferential operators, I. Math. Nachr. 167 (1994), 131–156.
E. Hebey, Nonlinear analysis on manifolds: Sobolev spaces and inequalities. AMS, Providence, Rhode Island 1999.
E. Hebey, Sobolev spaces on Riemannian Manifolds. LNM 1635, Springer, Berlin 1996.
E. Hebey and M. Vaugon, Sobolev spaces in the presence of symmetries, J. Math. Pures Appl. 76 (1997), 859–881.
Th. Kuhn, H.-G. Leopold, W. Sickel, L. Skrzypczak, Entropy numbers of Sobolev embeddings of radial Besov spaces,(submitted).
V.I. Kondrachov, Certain properties of functions in the spaces L P, Dokl. Akad. Nauk SSSR 48 (1945), 563–566.
I. Kuzin and S. Pohozaev, Entire solutions of seinilinear elliptic equations. Birkhauser, Basel, 1997.
P.-L. Lions, Symetrie et compacite dans les espaces de Sobolev, J. Funct. Anal. 49 (1982), 315–334.
Y.V. Netrusov, Spaces of singularities of functions in spaces of Besov and LizorkinTriebel type, Trudy Mat. Ins. Stekl. 187 (1989), 162–177 (Russian) [English translation: Proc. Steklov Inst. Math. 3 (1990), 185–203].
J. Peetre, Espaces d’Interpolation et Theoreme de Soboleff, Ann. Inst. Fourier 16 (1966), 279–317.
T. Runst, W. Sickel, Sobolev spaces of Fractional Order,Nemytskij Operators and Nonlinear Partial Differential Equations. De Gruyter, Berlin, New York, 1996.
W. Sickel and L. Skrzypczak, Radial subspaces of Besov and Lizorkin-Triebel Classes: Extended Strauss Lemma and Compactness of Embedding, J. Fourier Anal. App. 6 (2000), 639–662.
W. Sickel and H. Triebel, Holder Inequality and Sharp Embeddings in Function Spaces of B spq and F spq type, Z. Anal. Anwendungen 14 (1995), 105–140.
L. Skrzypczak, Optimal atomic decompositions on manifolds and compactness of Sobolev embeddings, (to appear).
L. Skrzypczak, Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay properties, Revista Mat. Iberoamer. (to appear).
L. Skrzypczak, B. Tomasz, Compactness of embeddings of the Trudinger-Strichartz type for rotation invariant functions,Houston J. Math. 27 (2001), 633–647.
W.A. Strauss,Existence of solitary waves in higher dimensions, Comm in Math. Physics 55 (1977), 149–162.
R.S. Strichartz, A note on Trudinger’s extension of Sobolev’s inequality, Indiana Univ. Math. J. 58 (1972), 841–842.
H. Triebel, Approximation numbers and entropy numbers of embeddings of fractional Besov-Sobolev spaces in Orlicz spaces, Proc. London Math. Soc. 66 (1993), 589–618.
H. Triebel, Theory of Function Spaces. Birkhauser, Basel, 1983.
H. Triebel, Theory of Function Spaces II. Birkhauser, Basel, 1992.
N. Trudinger, On embedding into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473–483.
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Skrzypczak, L. (2003). Function Spaces in Presence of Symmetries: Compactness of Embeddings, Regularity and Decay of Functions. In: Haroske, D., Runst, T., Schmeisser, HJ. (eds) Function Spaces, Differential Operators and Nonlinear Analysis. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8035-0_33
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DOI: https://doi.org/10.1007/978-3-0348-8035-0_33
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