References
- Fujita H, Kato T. On the Navier–Stokes initial value problem. I. Arch Rational Mech Anal. 1964;16:269–315. doi: https://doi.org/10.1007/BF00276188
- Kato T. Strong Lp-solutions of the Navier-Stokes equation in Rm, with applications to weak solutions. Math Z. 1984;187:471–480. doi: https://doi.org/10.1007/BF01174182
- Meyer Y, Coifman RR. Opérateurs pseudo-différentiels et théorème de Calderón, in: (French) Séminaire d'Analyse Harmonique (1976–1977), pp. 28–40, Publ. Math. Orsay, No. 77–77, Dépt. Math., Orsay: Univ. Paris-Sud; 1977.
- Meyer Y, Coifman RR. Au delà des opérateurs pseudo-différentiels, (French) [Beyond pseudodifferential operators] With an English summary, Astérisque 57, Société Mathématique de France, Paris, 1978.
- Meyer Y, Coifman RR. Wavelets. Calderón–Zygmund and multilinear operators, Translated from the 1990 and 1991 French originals In: Salinger D, editor. Cambridge: Cambridge University Press; 1997. (Cambridge Studies in Advanced Mathematics; 48).
- Bony J-M. Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires (French) [Symbolic calculus and propagation of singularities for nonlinear partial differential equations]. Ann Sci École Norm Sup (4). 1981;14:209–246. doi: https://doi.org/10.24033/asens.1404
- Muscalu C, Tao T, Thiele C. Uniform estimates on multi-linear operators with modulation symmetry. Dedicated to the memory of Tom Wolff. J Anal Math. 2002;88:255–309. doi: https://doi.org/10.1007/BF02786579
- Grafakos L, Kalton NJ. The Marcinkiewicz multiplier condition for bilinear operators. Studia Math. 2001;146:115–156. doi: https://doi.org/10.4064/sm146-2-2
- Gilbert JE, Nahmod AR. Bilinear operators with non-smooth symbol. I. J Fourier Anal Appl. 2001;7:435–467. doi: https://doi.org/10.1007/BF02511220
- Gilbert JE, Nahmod AR. Lp-boundedness for time-frequency paraproducts. II. J Fourier Anal Appl. 2002;8:109–172. doi: https://doi.org/10.1007/s00041-002-0006-5
- Bényi Á, Maldonado D, Nahmod AR. Bilinear paraproducts revisited. Math Nachr. 2010;283:1257–1276. doi: https://doi.org/10.1002/mana.200710157
- David G, Journé J-L. A boundedness criterion for generalized Calderón–Zygmund operators. Ann Math (2). 1984;120:371–397. doi: https://doi.org/10.2307/2006946
- Chow YS, Teicher H. Probability theory. independence, interchangeability, martingales. 3rd ed. New York: Springer-Verlag; 1997. (Springer Texts in Statistics).
- Germain P, Masmoudi N, Shatah J. Global solutions for the gravity water waves equation in dimension 3. Ann Math (2). 2012;175:691–754. doi: https://doi.org/10.4007/annals.2012.175.2.6
- Germain P, Masmoudi N, Shatah J. Global solutions for 2D quadratic Schrödinger equations. J Math Pures Appl (9). 2012;97:505–543. doi: https://doi.org/10.1016/j.matpur.2011.09.008
- Bényi Á, Maldonado D, Naibo V. What is ··· a paraproduct? Notices Amer Math Soc. 2010;57:858–860.
- Bernicot F. Uniform estimates for paraproducts and related multilinear multipliers. Rev Mat Iberoam. 2009;25:1055–1088. doi: https://doi.org/10.4171/RMI/589
- Bernicot F. A T(1)-theorem in relation to a semigroup of operators and applications to new paraproducts. Trans Amer Math Soc. 2012;364:6071–6108. doi: https://doi.org/10.1090/S0002-9947-2012-05609-1
- Bernicot F. Fiber-wise Calderón–Zygmund decomposition and application to a bi-dimensional paraproduct. Illinois J Math. 2012;56:415–422. doi: https://doi.org/10.1215/ijm/1385129956
- Bonami A, Grellier S, Ky LD. Paraproducts and products of functions in BMO (Rn) and H1(Rn) through wavelets. J Math Pures Appl (9). 2012;97:230–241. doi: https://doi.org/10.1016/j.matpur.2011.06.002
- Ky LD. Bilinear decompositions for the product space HL1×BMOL. Math Nachr. 2014;287:1288–1297. doi: https://doi.org/10.1002/mana.201200101
- Ky LD. Bilinear decompositions and commutators of singular integral operators. Trans Amer Math Soc. 2013;365:2931–2958. doi: https://doi.org/10.1090/S0002-9947-2012-05727-8
- Ky LD. Endpoint estimates for commutators of singular integrals related to Schrödinger operators. Rev Mat Iberoam. 2015;31:1333–1373. doi: https://doi.org/10.4171/RMI/871
- Coifman RR, Weiss G. Analyse harmonique non-commutative sur certains espaces homogènes (French) Étude de certaines intégrales singulières. Berlin-New York: Springer-Verlag; 1971. (Lecture Notes in Mathematics; 242).
- Coifman RR, Weiss G. Extensions of Hardy spaces and their use in analysis. Bull Amer Math Soc. 1977;83:569–646. doi: https://doi.org/10.1090/S0002-9904-1977-14325-5
- Fu X, Yang D, Yang S. Endpoint boundedness of linear commutators on local Hardy spaces over metric measure spaces of homogeneous type. J Geom Anal. 2020. doi: https://doi.org/10.1007/s12220-020-00429-8
- Nakai E, Yabuta K. Pointwise multipliers for functions of weighted bounded mean oscillation on spaces of homogeneous type. Math Japon. 1997;46:15–28.
- Auscher P, Hytönen T. Orthonormal bases of regular wavelets in spaces of homogeneous type. Appl Comput Harmon Anal. 2013;34:266–296. doi: https://doi.org/10.1016/j.acha.2012.05.002
- Han Y, Müller D, Yang D. A theory of Besov and Triebel-Lizorkin spaces on metric measure spaces modeled on Carnot–Carathéodory spaces. Abstr Appl Anal. 2008; Art. ID 893409:1–250. doi: https://doi.org/10.1155/2008/893409
- Han Y, Müller D, Yang D. Littlewood–Paley characterizations for Hardy spaces on spaces of homogeneous type. Math Nachr. 2006;279:1505–1537. doi: https://doi.org/10.1002/mana.200610435
- Yang D, Zhou Y. New properties of Besov and Triebel-Lizorkin spaces on RD-spaces. Manuscripta Math. 2011;134:59–90. doi: https://doi.org/10.1007/s00229-010-0384-y
- Deng D, Han Y. Harmonic analysis on spaces of homogeneous type. Berlin: Springer-Verlag; 2009. (Lecture Notes in Mathematics; 1966).
- Macías RA, Segovia C. A decomposition into atoms of distributions on spaces of homogeneous type. Adv Math. 1979;33:271–309. doi: https://doi.org/10.1016/0001-8708(79)90013-6
- Bui TA, Duong XT, Ly FK. Maximal function characterizations for new local Hardy type spaces on spaces of homogeneous type. Trans Amer Math Soc. 2018;370:7229–7292. doi: https://doi.org/10.1090/tran/7289
- Bui TA, Duong XT, Ly FK. Maximal function characterizations for Hardy spaces on spaces of homogeneous type with finite measure and applications. J Funct Anal. 2020;278:108423. 55 pp doi: https://doi.org/10.1016/j.jfa.2019.108423
- Yang D, Zhou Y. Radial maximal function characterizations of Hardy spaces on RD-spaces and their applications. Math Ann. 2010;346:307–333. doi: https://doi.org/10.1007/s00208-009-0400-2
- Grafakos L, Liu L, Maldonado D, et al. Multilinear analysis on metric spaces. Dissertationes Math. 2014;497:1–121. doi: https://doi.org/10.4064/dm497-0-1
- Grafakos L, Liu L, Yang D. Boundedness of paraproduct operators on RD-spaces. Sci China Math. 2010;53:2097–2114. doi: https://doi.org/10.1007/s11425-010-4042-3
- Hu G, Yang D, Zhou Y. Boundedness of singular integrals in Hardy spaces on spaces of homogeneous type. Taiwanese J Math. 2009;13:91–135. doi: https://doi.org/10.11650/twjm/1500405274
- Bui H-Q, Bui TA, Duong XT. Weighted Besov and Triebel–Lizorkin spaces associated to operators and applications. Forum Math Sigma. 2020;8:e11. 95 pp doi: https://doi.org/10.1017/fms.2020.6
- Bui TA, Duong XT. Sharp weighted estimates for square functions associated to operators on spaces of homogeneous type. J Geom Anal. 2020;30:874–900. doi: https://doi.org/10.1007/s12220-019-00173-8
- Bui TA, Duong XT, Ky LD. Hardy spaces associated to critical functions and applications to T1 theorems. J Fourier Anal Appl. 2020;26: Article number 27. 67 pp doi: https://doi.org/10.1007/s00041-020-09731-z
- Han Ya., Han Yo., Li J. Geometry and Hardy spaces on spaces of homogeneous type in the sense of Coifman and Weiss. Sci China Math. 2017;60:2199–2218. doi: https://doi.org/10.1007/s11425-017-9152-4
- Han Y, Li J, Ward LA. Hardy space theory on spaces of homogeneous type via orthonormal wavelet bases. Appl Comput Harmon Anal. 2018;45:120–169. doi: https://doi.org/10.1016/j.acha.2016.09.002
- He Z, Han Y, Li J, et al. A complete real-variable theory of Hardy spaces on spaces of homogeneous type. J Fourier Anal Appl. 2019;25:2197–2267. doi: https://doi.org/10.1007/s00041-018-09652-y
- He Z, Liu L, Yang D, et al. New Calderón reproducing formulae with exponential decay on spaces of homogeneous type. Sci China Math. 2019;62:283–350. doi: https://doi.org/10.1007/s11425-018-9346-4
- He Z, Yang D, Yuan W. Real-variable characterizations of local Hardy spaces on spaces of homogeneous type. Math Nachr. 2019. Available from: https://doi.org/https://doi.org/10.1002/mana.201900320.
- Fu X, Yang D, Liang Y. Products of functions in BMO (X) and Hat1(X) via wavelets over spaces of homogeneous type. J Fourier Anal Appl. 2017;23:919–990. doi: https://doi.org/10.1007/s00041-016-9483-9
- Han Ya., Han Yo., Li J. Criterion of the boundedness of singular integrals on spaces of homogeneous type. J Funct Anal. 2016;271:3423–3464. doi: https://doi.org/10.1016/j.jfa.2016.09.006
- Liu L, Chang D-C, Fu X, et al. Endpoint boundedness of commutators on spaces of homogeneous type. Appl Anal. 2017;96:2408–2433. doi: https://doi.org/10.1080/00036811.2017.1341628
- Liu L, Chang D-C, Fu X, et al. Endpoint estimates of linear commutators on Hardy spaces over spaces of homogeneous type. Math Meth Appl Sci. 2018;41:5951–5984. doi: https://doi.org/10.1002/mma.5112
- Liu L, Yang D, Yuan W. Bilinear decompositions for products of Hardy and Lipschitz spaces on spaces of homogeneous type. Diss Math (Rozprawy Mat). 2018;533:1–93.
- Han Ya., Han Yo., He Z, et al. Geometric characteriztions of embedding theorems – for Sobolev, Besov, and Triebel–Lizorkin spaces on spaces of homogeneous type – via orthonormal wavelets. J Geom Anal (to appear).
- He Z, Wang F, Yang D. Wavelet characterizations of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type and their applications. Submitted.
- Wang F, Han Y, He Z, et al. Besov spaces and Triebel–Lizorkin spaces on spaces of homogeneous type with their applications to a boundedness of Calderón–Zygmund operators. Submitted.
- Zhou X, He Z, Yang D. Real-variable characterizations of Hardy–Lorentz spaces on spaces of homogeneous type with applications to real interpolation and boundedness of Calderón–Zygmund operators. Anal Geom Metr Spaces. 2020. Available from: https://doi.org/https://doi.org/10.1515/agms-2020-0109.
- Fu X, Chang D-C, Yang D. Recent progress in bilinear decompositions. Appl Anal Optim. 2017;1:153–210.
- Fu X, Ma T, Yang D. Real-variable characterizations of Musielak–Orlicz Hardy spaces on spaces of homogeneous type. Ann Acad Sci Fenn Math. 2020;45:343–410. doi: https://doi.org/10.5186/aasfm.2020.4519
- Chang D-C, Fu X, Yang D. Boundedness of paraproducts on spaces of homogeneous type II. Appl Anal. 2020. Available from: https://doi.org/https://doi.org/10.1080/00036811.202.1800654.
- Hytönen T, Kairema A. Systems of dyadic cubes in a doubling metric space. Colloq Math. 2012;126:1–33. doi: https://doi.org/10.4064/cm126-1-1
- Hytönen T, Tapiola O. Almost Lipschitz-continuous wavelets in metric spaces via a new randomization of dyadic cubes. J Approx Theory. 2014;185:12–30. doi: https://doi.org/10.1016/j.jat.2014.05.017
- Grafakos L. Modern Fourier analysis. 3rd ed. New York: Springer; 2014. (Graduate Texts in Mathematics; 250).