Traces of Muckenhoupt weighted function spaces in case of distant singularities

References

[1] H. Abels, M. Krbec and K. Schumacher, On the trace space of a Sobolev space with a radial weight, J. Funct. Spaces Appl. 6 (2008), no. 3, 259–276. 10.1155/2008/986720Search in Google Scholar

[2] K. F. Andersen and R. T. John, Weighted inequalities for vector-valued maximal functions and singular integrals, Studia Math. 69 (1980/81), no. 1, 19–31. 10.4064/sm-69-1-19-31Search in Google Scholar

[3] M. Bownik, Atomic and molecular decompositions of anisotropic Besov spaces, Math. Z. 250 (2005), no. 3, 539–571. 10.1007/s00209-005-0765-1Search in Google Scholar

[4] M. Bownik and K. P. Ho, Atomic and molecular decompositions of anisotropic Triebel–Lizorkin spaces, Trans. Amer. Math. Soc. 358 (2006), no. 4, 1469–1510. 10.1090/S0002-9947-05-03660-3Search in Google Scholar

[5] H.-Q. Bui, Weighted Besov and Triebel spaces: Interpolation by the real method, Hiroshima Math. J. 12 (1982), no. 3, 581–605. 10.32917/hmj/1206133649Search in Google Scholar

[6] H.-Q. Bui, Characterizations of weighted Besov and Triebel-Lizorkin spaces via temperatures, J. Funct. Anal. 55 (1984), no. 1, 39–62. 10.1016/0022-1236(84)90017-XSearch in Google Scholar

[7] H.-Q. Bui, M. Paluszyński and M. H. Taibleson, A maximal function characterization of weighted Besov–Lipschitz and Triebel–Lizorkin spaces, Studia Math. 119 (1996), no. 3, 219–246. Search in Google Scholar

[8] H.-Q. Bui, M. Paluszyński and M. H. Taibleson, Characterization of the Besov–Lipschitz and Triebel–Lizorkin spaces. The case q<1, J. Fourier Anal. Appl. 3 (1997), no. Special Issue, 837–846. 10.1007/BF02656489Search in Google Scholar

[9] V. I. Burenkov and M. L. Gol’dman, Extension of functions from Lp (in Russian), Trudy Mat. Inst. Steklov. 150 (1979), 31–51, 321. Search in Google Scholar

[10] K. J. Falconer, The Geometry of Fractal Sets, Cambridge Tracts in Math. 85, Cambridge University Press, Cambridge, 1986. Search in Google Scholar

[11] R. Farwig and H. Sohr, Weighted Lq-theory for the Stokes resolvent in exterior domains, J. Math. Soc. Japan 49 (1997), no. 2, 251–288. 10.2969/jmsj/04920251Search in Google Scholar

[12] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), no. 4, 777–799. 10.1515/9781400827268.385Search in Google Scholar

[13] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), no. 1, 34–170. 10.1016/0022-1236(90)90137-ASearch in Google Scholar

[14] M. Frazier and S. Roudenko, Matrix-weighted Besov spaces and conditions of Ap type for 0<p≤1, Indiana Univ. Math. J. 53 (2004), no. 5, 1225–1254. 10.1512/iumj.2004.53.2483Search in Google Scholar

[15] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, Amsterdam, 1985. Search in Google Scholar

[16] M. L. Gol’dman, Extension of functions in Lp⁢(ℝm) to a space of higher dimension (in Russian), Mat. Zametki 25 (1979), no. 4, 513–520. Search in Google Scholar

[17] D. D. Haroske, Dichotomy in Muckenhoupt weighted function space: A fractal example, Spectral Theory, Function Spaces and Inequalities, Oper. Theory Adv. Appl. 219, Birkhäuser, Basel (2012), 69–89. 10.1007/978-3-0348-0263-5_5Search in Google Scholar

[18] D. D. Haroske and I. Piotrowska, Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis, Math. Nachr. 281 (2008), no. 10, 1476–1494. 10.1002/mana.200510690Search in Google Scholar

[19] D. D. Haroske and H.-J. Schmeisser, On trace spaces of function spaces with a radial weight: The atomic approach, Complex Var. Elliptic Equ. 55 (2010), no. 8–10, 875–896. 10.1080/17476930903276050Search in Google Scholar

[20] D. D. Haroske and L. Skrzypczak, Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights. I, Rev. Mat. Complut. 21 (2008), no. 1, 135–177. 10.5209/rev_REMA.2008.v21.n1.16447Search in Google Scholar

[21] D. D. Haroske and L. Skrzypczak, Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights. II: General weights, Ann. Acad. Sci. Fenn. Math. 36 (2011), no. 1, 111–138. 10.5186/aasfm.2011.3607Search in Google Scholar

[22] D. D. Haroske and L. Skrzypczak, Entropy numbers of embeddings of function spaces with Muckenhoupt weights. III: Some limiting cases, J. Funct. Spaces Appl. 9 (2011), no. 2, 129–178. 10.1155/2011/928962Search in Google Scholar

[23] A. Jonsson and H. Wallin, Function spaces on subsets of ℝn, Math. Rep. 2 (1984), no. 1. Search in Google Scholar

[24] V. M. Kokilashvili, Maximum inequalities and multipliers in weighted Lizorkin–Triebel spaces (in Russian), Dokl. Akad. Nauk SSSR 239 (1978), no. 1, 42–45. Search in Google Scholar

[25] B. Muckenhoupt, Hardy’s inequality with weights, Studia Math. 44 (1972), 31–38. 10.4064/sm-44-1-31-38Search in Google Scholar

[26] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. 10.1090/S0002-9947-1972-0293384-6Search in Google Scholar

[27] B. Muckenhoupt, The equivalence of two conditions for weight functions, Studia Math. 49 (1973/74), 101–106. 10.4064/sm-49-2-101-106Search in Google Scholar

[28] S. M. Nikol’skiĭ, Approximation of Functions of Several Variables and Embedding Theorems, Nauka, Moscow, 1969; 2nd ed., Nauka, Moscow, 1977. English translation: Grundlehren Math. Wiss. 205, Springer, Berlin, 1975. Search in Google Scholar

[29] J. Peetre, The trace of Besov space – A limiting case, Technical report, University Lund, Lund, 1975. Search in Google Scholar

[30] J. Peetre, A counterexample connected with Gagliardo’s trace theorem, Comment. Math. Special Issue 2 (1979), 277–282. Search in Google Scholar

[31] I. Piotrowska, Traces on fractals of function spaces with Muckenhoupt weights, Funct. Approx. Comment. Math. 36 (2006), 95–117. 10.7169/facm/1229616444Search in Google Scholar

[32] I. Piotrowska, Weighted function spaces and traces on fractals, PhD thesis, Friedrich-Schiller-Universität Jena, Jena, 2006. Search in Google Scholar

[33] S. Roudenko, Matrix-weighted Besov spaces, Trans. Amer. Math. Soc. 355 (2003), no. 1, 273–314. 10.1090/S0002-9947-02-03096-9Search in Google Scholar

[34] S. Roudenko, Duality of matrix-weighted Besov spaces, Studia Math. 160 (2004), no. 2, 129–156. 10.4064/sm160-2-3Search in Google Scholar

[35] V. S. Rychkov, Littlewood–Paley theory and function spaces with Aploc weights, Math. Nachr. 224 (2001), 145–180. 10.1002/1522-2616(200104)224:1<145::AID-MANA145>3.0.CO;2-2Search in Google Scholar

[36] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Math. Ser. 43, Princeton University Press, Princeton, 1993. 10.1515/9781400883929Search in Google Scholar

[37] J.-O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer, Berlin, 1989. 10.1007/BFb0091154Search in Google Scholar

[38] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure Appl. Math. 123, Academic Press, Orlando, 1986. Search in Google Scholar

[39] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland Math. Library 18, North-Holland, Amsterdam, 1978. Search in Google Scholar

[40] H. Triebel, Theory of Function Spaces, Monogr. Math. 78, Birkhäuser, Basel, 1983; reprinted 2010. 10.1007/978-3-0346-0416-1Search in Google Scholar

[41] H. Triebel, Theory of Function Spaces. II, Monogr. Math. 84, Birkhäuser, Basel, 1992; reprinted 2010. 10.1007/978-3-0346-0419-2Search in Google Scholar

[42] H. Triebel, Fractals and Spectra. Related to Fourier Analysis and Function Spaces, Monogr. Math. 91, Birkhäuser, Basel, 1997; reprinted 2011. 10.1007/978-3-0348-0034-1_3Search in Google Scholar

[43] H. Triebel, The Structure of Functions, Modern Birkhäuser Classics, Birkhäuser, Basel, 2001. Search in Google Scholar

[44] H. Triebel, Theory of Function Spaces. III, Monogr. Math. 100, Birkhäuser, Basel, 2006. Search in Google Scholar

[45] H. Triebel, Function Spaces and Wavelets on Domains, EMS Tracts Math. 7, European Mathematical Society (EMS), Zürich, 2008. 10.4171/019Search in Google Scholar

[46] H. Triebel and H. Winkelvoß, A Fourier analytical characterization of the Hausdorff dimension of a closed set and of related Lebesgue spaces, Studia Math. 121 (1996), no. 2, 149–166. 10.4064/sm-121-2-149-166Search in Google Scholar

[47] H. Triebel and H. Winkelvoß, Intrinsic atomic characterizations of function spaces on domains, Math. Z. 221 (1996), no. 4, 647–673. 10.1007/PL00004525Search in Google Scholar