Interpolation of bilinear operators between Quasi-Banach spaces

Positivity

Volumn 10, Issue 3, 2006, Pages 409-429

  Grafakos, Loukas ^a   Mastyło, Mieczysław ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b ADAM MICKIEWICZ UNIVERSITY   (Poland)

Author keywords

Bilinear operators; Calder n Lozanovsky spaces; Interpolation; Lorentz Zygmund spaces; Multilinear interpolation; Quasi Banach spaces

Indexed keywords

EID: 33746725261     PISSN: 13851292     EISSN: 15729281     Source Type: Journal    
DOI: 10.1007/s11117-005-0034-x     Document Type: Article

References (29)

1. S.V. Astashkin, On Interpolation of Bilinear Operators by the Real Method of Interpotation, Mat. Zametki, 52 (1992), 15-24 (Russian).
2. J. Bergh, J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin (1976).
3. A.Yu. Brudnyi, N.Ya. Krugljak, Interpolation Functors and Interpolation Spaces I, North-Holland, Amsterdam, (1991).
4. A.P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), 113-190.
5. M. Cwikel, J. Peetre, Abstract K and J spaces, J. Math. Pures. Appl., 60 (1981), 1-50.
6. R.R. Coifman, Y. Meyer, Commutateurs d'intègrales singulières et opérateurs multilinéaires, Ann. Inst. Fourier (Grenoble), 28 (1978), 177-202.
7. J. Gilbert, A. Nahrnod, Bilinear operators with non-smooth symbols, J. Fourier Anal. Appl. 7 (2001), 437-469.
8. L. Grafakos, R. Torres, Multilinear Calderón Zygmund theory, Adv. in Math. 40 (1996), 344-351.
9. L. Grafakos, N.J. Kalton, The Marcinkiewicz multiplier condition for bilinear operators, Studia Math. 146 (2001), 115-156.
10. L. Grafakos, N.J. Kalton, Multilinear Calderón-Zygmund operators on Hardy spaces, Collect. Math., 52 (2001), 169-179.
11. J. Gustavsson, A function parameter in connetion with interpolation of Banach spaces, Math. Scarid., 42 (1978), 289-305.
12. J. Gustavsson, J. Peetre, Interpolation of Orlicz spaces, Studia Math., 60 (1977), 33-59.
13. N.J. Kalton, Convexity conditions for non-locally convex lattices, Glasgow Math. J., 25 (1984), 141-152.
14. N.J. Kalton, N.T. Peck, J.W. Roberts, An F-space Sampler, London Math. Soc. Lecture Notes 89, Cambridge University Press, (1985).
15. N.J. Kalton, Plurisubharmonic functions on quasi-Banach spaces, Studia Math. 84 (1986), 297-324.
16. G. Kenig, E.M. Stein, Multilinear estimates and fractional integration, Math. Res. Lett. 6 (1999), 1-15.
17. S.G. Krein, Yu.I. Petunin, E.M. Semenov, Interpolation of Linear Operators, Nauka, Moscow, 1978 (in Russian); English transl.: Amer. Math. Soc., Providence, (1982).
18. p bounds for the bilinear Hubert transform, p > 2, Ann. of Math., 146 (1997), 693-724.
19. M.T. Lacey, C.M. Thiele, On Calderóns conjecture, Ann. of Math., 149 (1999), 475-496.
20. J.L. Lions, J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Etudes Sci. Publ. Math., 19 (1964), 5-68.
21. G.Ya. Lozanovsky, On some Banach lattices IV, Sibirsk. Mat. Z. 14 (1973), 140-155 (in Russian);
22. English transl.: Siberian. Math. J. 14 (1973), 97-108.
23. M. Mastylo, On interpolation of some quasi-Banach spaces, J. Math. Anal. Appl. 147 (1990), 403-419.
24. M. Mastylo, On interpolation of bilinear operators, J. Funct. Anal., 214 (2004), 260-283.
25. M. Mastylo, Interpolation methods of means and orbits, Studia Math., 17 (2005), 53-175.
26. C. Merucci, Application of interpolation with function parameter to Lorentz, Sobolev and Besov spaces, In: Interpolation Spaces and Allied Topics in Analysis, Lecture Notes in Math. 1070 (1984), 183-201.
27. P. Nilsson, Interpolation of Banach lattices, Studia Math., 82 (1985), 135-154.
28. Y. Sagher, Interpolation of r-Banach spaces, Studia Math., 26 (1966), 45-70.
29. M. Zafran, A multilinear interpolation theorem, Studia Math., 62 (1978), 107-124.