Duals of Besov and Triebel-Lizorkin Spaces Associated with Operators

Springer Science and Business Media LLC - Tập 57 - Trang 547-577 - 2022
Athanasios G. Georgiadis1, George Kyriazis2
1Faculty of Engineering, Mathematics and Science, Trinity College of Dublin, Dublin, Ireland
2Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus

Tóm tắt

We consider the general framework of a metric measure space satisfying the doubling volume property, associated with a non-negative self-adjoint operator, whose heat kernel enjoys standard Gaussian localization. We study the dual spaces of the classical and nonclassical Besov and Triebel-Lizorkin spaces on this setting. Our results generalize those on Euclidean spaces and are new on several setups of independent interest; the sphere, the ball, more general Riemannian manifolds and other settings.

Tài liệu tham khảo

Bui, H.-Q., Bui, T.A., Duong, X.T.: Weighted Besov and Triebel-Lizorkin spaces associated with operators and applications. Forum Math. Sigma 8(e11), 95 (2020) Bownik, M.: Duality and interpolation of anisotropic Triebel?Lizorkin spaces. Math. Z. 259, 131–169 (2008) Castillo, I., Kerkyacharian, G., Picard, D.: Thomas Bayes walk on manifolds. Probab. Theory Relat. Fields 158(3–4), 665–710 (2014) Cleanthous, G., Georgiadis, A.G., Kerkyacharian, G., Petrushev, P., Picard, D.: Kernel and wavelet density estimators on manifolds or more general metric spaces. Bernoulli 26(3), 1832–1862 (2020) Coifman, R., Weiss, G.: Extensions of Hardy spaces and their use in analysis. Bull. Am. Math. Soc. 83(4), 569–645 (1977) Coifman, R., Weiss, G.: Analyse harmonique non-commutative sur certains espaces homogenes. Lecture Notes in Math, vol. 242. Springer-Verlag, Berlin and New York (1971) Coulhon, T., Kerkyacharian, G., Petrushev, P.: Heat kernel generated frames in the setting of Dirichlet spaces. J. Fourier Anal. Appl. 18(5), 995–1066 (2012) Dai, F., Xu, Y.: Approximation theory and harmonic analysis on spheres and balls. Springer Monographs in Mathematics, Springer, New York (2013) Dekel, S., Kerkyacharian, G., Kyriazis, G., Petrushev, P.: Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators. Studia Math. 225(2), 115–163 (2014) Dekel, S., Kerkyacharian, G., Kyriazis, G., Petrushev, P.: Hardy spaces associated with non-negative self-adjoint operators. Studia Math. 239(1), 1–54 (2017) Frazier, M., Jawerth, B.: Decomposition of Besov Spaces. Indiana Univ. Math. J. 34, 777–799 (1985) Georgiadis, A.G., Kyriazis, G.: Embeddings between Triebel-Lizorkin spaces on metric spaces associated with operators. Anal. Geom. Metr. Spaces 8(1), 418–429 (2020) Georgiadis, A.G., Kerkyacharian, G., Kyriazis, G., Petrushev, P.: Homogeneous Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators. J. Math. Anal. Appl. 449(2), 1382–1412 (2017) Georgiadis, A.G., Kerkyacharian, G., Kyriazis, G., Petrushev, P.: Atomic and molecular decomposition for homogeneous spaces of distributions associated to non-negative self-adjoint operators. J. Fourier Anal. Appl. 25(6), 3259–3309 (2019) Georgiadis, A.G., Nielsen, M.: Pseudodifferential operators on spaces of distributions associated with non-negative self-adjoint operators. J. Fourier Anal. Appl. 23(2), 344–378 (2017) Georgiadis, A.G., Nielsen, M.: Spectral multipliers on spaces of distributions associated with non-negative self-adjoint operators. J. Approx. Theory 234, 1–19 (2018) Jawerth, B.: Some observations on Besov and Lizorkin-Triebel spaces. Math. Scand. 40(1), 94–104 (1977) Kerkyacharian, G., Ogawa, S., Petrushev, P., Picard, D.: Regularity of Gaussian processes on Dirichlet spaces. Constr. Approx. 47(2), 277–320 (2018) Kerkyacharian, G., Petrushev, P.: Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces. Trans. Am. Math. Soc. 367, 121–189 (2015) Kerkyacharian, G., Petrushev, P., Xu, Y.: Gaussian bounds for the weighted heat kernels on the interval, ball and simplex. Constr. Approx. 51, 73–122 (2020) Li, B., Bownik, M., Yang, D., Yuan, W.: Duality of weighted anisotropic Besov and Triebel-Lizorkin spaces. Positivity 16, 213–244 (2012) Liu, L., Yang, D., Yuan, W.: Besov-type and Triebel-Lizorkin-type spaces associated with heat kernels. Collect. Math. 67(2), 247–310 (2016) Triebel, H.: Spaces of distributions of Besov type on Euclidean \(n\)-space. Duality, interpolation. Ark. Mat. 11, 13–64 (1973) Triebel, H.: Theory of function spaces. Monographs in Math, vol. 78. Birkhäuser Verlag, Basel (1983) Verbitsky, I.: Imbedding and multiplier theorems for discrete littlewood? Paley spaces. Pac. J. Math. 176, 529–556 (1996)