Abstract
Let L be an elliptic operator, we give arguments about the duality estimate between Morrey spaces and its pre-dual spaces characterized by the heat kernel associated to L that is given in [6],[8].
Similar content being viewed by others
References
Auscher, P. and Tchamitchian, P., Square Root Problem for Divergence Operators and Related Topics, Asterisque, 249(1998)
Coifman, R., Meyer, Y. and Stein, E. M., Some New Function Spaces and Their Applications to Harmonic Analysis, J. Funct. Anal., 62(1985), 304–335.
Deng, D. G., On a Generalized Carleson Inequality, Studia. Math., 78(1984), 245–251.
Deng, D. G., Xu, M. and Yan, L. X., Fractional Integration Associated to Higher Order Elliptic Operators, Chinease. Ann. of Math(B), 26:2(2005), 229–238.
Duong, X. T. and Alan. MacIntosh, Singular Integral Operators with Non-smooth Kernels on Irregular Domains, Rev. Mat. Iberoamericana., 15:2(1999), 233–265.
Duong, X. T. and Yan, L. X., Duality of Hardy and BMO Spaces Associated with Operators with Heat Kernel Bounds, Jour. Amer. Math. Soc, 18(2005), 943–973.
Duong, X. T. and Yan, L. X., New Function Spaces of BMO type, John-Nirenberg inequality,interpolation and applications, Comm. Pure Appl. Math., 58(2005), 1375–1420.
Duong, X. T., Xiao, J. and Yan, L. X., Old and New Morrey Spaces with Heat Kernel Bounds, J. Fourier. Anal. and. Appl., 13(2007), 87–111.
Martell, J. M., Sharp Maximal Functions Associated with Approximations of the Identity in Spaces of Homogeneous type and Applications, Studia Math., 161(2004), 113–145.
Alan. McIntosh, Operators which have an H ∞-calculus, Miniconference on Operator Theory and Partial Differential Equations, Proc. Center. Math.Analysis., ANU, Canberra, 14 (1986),210–231.
Shen, Z. W., On Fundamental Solution of Generalized Schödinger Operators, J. Funct. Anal., 167(1999), 521–564.
Campanato, S., Proprietà di Una Foiglia di Spazi Funzionali, Ann. Sci. Norm. Sup. Pisa, 18(1964), 137–160.
Coifman, R. and Weiss, G., Analyse Harmonique Non-commutative Sur Certains Espaces Homogenes, Lectue. Notes. in. Math, Springer-Verlag, Berlin, 242(1971).
Zorko, C., The Morrey Space, Proc. of. AMS, 98(1986), 586–592.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, M. The duality between Morrey spaces and its pre-dual spaces characterized by heat kernel. Anal. Theory Appl. 25, 71–78 (2009). https://doi.org/10.1007/s10496-009-0071-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10496-009-0071-6