Remark on borderline traces of Besov and Triebel-Lizorkin spaces on noncompact hypersurfaces

• Autorzy: Skrzypczak L. , Tomasz B.

Identyfikatory

DOI

10.14708/cm.v53i2.793

• Języki publikacji: EN

Abstrakty

EN

We investigate borderline traces of Besov and Triebel-Lizorkin spaces. The function spaces are defined on noncompact Riemannian manifolds with bounded geometry. We described spaces of traces on noncompact submanifolds that are also of bounded geometry.

Słowa kluczowe

EN

Besov spaces; Triebel-Lizorkin spaces; Riemannian manifolds of bounded geometry; traces

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol. 53, No. 2
• Strony: 193--209
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Skrzypczak L.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, Poznan 61-614

autor

Tomasz B.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, Poznan 61-614

Bibliografia

• [1] T. Aubin, Nonlinear problems in Riemannian Geometry, Springer Verlag, 1998.
• [2] V.I. Burenkov and M.L. Goldman, Extension of functions from Lp. (Russian) Studies in the theory of differentiable functions of several variables and its applications, VII. Trudy Mat. Inst. Steklov. 150 (1979), 31-51.
• [3] M. Frazier and B. Jawerth, Decomposition of Besov spaces. Indiana Univ. Math. J. 34 (1985), 777-799.
• [4] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces. J. Funct. Anal. 93 (1990), 34-170.
• [5] S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry. Springer Verlag 1992.
• [6] M.L. Goldman, Extension of functions in Lp(Rm) to a space of higher dimension, (Russian) Mat. Zametki 25 (1979), 513-520.
• [7] N. Gro_e and C. Schneider, Sobolev spaces on Riemannian manifolds with bounded geometry: General coordinates and traces, Math. Nachr. DOI 10.1002/mana.201300007.
• [8] E. Hebey, Nonlinear analysis on manifolds: Sobolev spaces and inequalities, AMS, Providence, Rhode Island 1999.
• [9] M.A. Shubin, Spectral theory of elliptic operators on non–compact manifolds. Astérisque 207 (1992), 37-108.
• [10] C. Schneider, Trace operators in Besov and Triebel-Lizorkin spaces, Z. Anal. Anwend. 29 (2010), 275–302.
• [11] 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.
• [12] L. Skrzypczak, Atomic decompositions on manifolds with bounded geometry. Forum Math. 10 (1998), 19-38.
• [13] L. Skrzypczak, Heat extensions, optimal atomic decompositions and Sobolev embeddings on in presence of symmetries on manifolds, Math. Zeitsch. 243 (2003), 745-773.
• [14] L. Skrzypczak, Traces of function spaces of Fs p,q –Bs p,q type on submanifolds, Math. Nachr. 146 (1990), 137-147.
• [15] H. Triebel, Diffeomorphism properties and pointwise multipliers for function spaces, in: Function spaces (Poznan, 1986), 75-84, Teubner-Texte Math., 103, Teubner, Leipzig, 1988.
• [16] H. Triebel, Spaces of Besov-Hardy-Sobolev Type on Complete Riemannian manifolds, Arkiv Mat. 24 (1986), 300-337.
• [17] H. Triebel, Theory of Function Spaces. Birkhäuser, Basel 1983.
• [18] H. Triebel, Theory of Function Spaces II. Birkhäuser, Basel 1992.