Embedding of vector-valued Morrey spaces and separable differential operators

Agarwal, R.P., O’ Regan, D., Shakhmurov, V.B.: Separable anisotropic differential operators in weighted abstract spaces and applications. J. Math. Anal. Appl. 338(2), 970–983 (2008) Amann, H.: Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications. Math. Nachr. 186, 5–56 (1997) Besov, O.V., Ilin, V.P., Nikolskii, S.M.: Integral Representations of Functions and Embedding Theorems. Nauka, Moscow (1975) Bianca, C.: Thermostatted kinetic equations as models for complex systems in physics and life sciences. Phys. Life Rev. 9(4), 359–399 (2012) Bianca, C.: On set of nonlinearity in thermostatted active particles models for complex systems. Nonlinear Anal. Real World Appl. 13(6), 2593–2608 (2012) Bianca, C.: Modeling complex systems by functional subsystems representation and thermostatted-KTAP methods. Appl. Math. Inf. Sci. 6, 495–499 (2012) Bourgain, J.: Some remarks on Banach spaces in which martingale differences are unconditional. Ark. Mat. 21(2), 163–168 (1983) Burenkov, V.I.: Recent progress in studying boundedness of classical operators of real analysis in general Morrey-type spaces. I. Eurasian Math. J. 3(3), 11–32 (2012) Burenkov, V.I., Guliyev, V.S.: Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces. Studia Math. 163(2), 157–176 (2004) Burenkov, V.I., Guliyev, V.S.: Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces. Potential Anal. 30(3), 211–249 (2009) Burkholder: A geometric conditions that implies the existence of certain singular integrals of Banach-space-valued functions. In: Conference on Harmonic Analysis in Honor of Antoni Zygmund, Vol. I, II (Chicago, IL), pp. 270–286 (1981) Clement, P., Pagter, B., de Sukochev, F.A., Witvliet, H.: Schauder decomposition and multiplier theorems. Studia Math. 138(2), 135–163 (2000) Coifman, R., Rochberg, R.: Another characterization of BMO. Proc. Am. Math. Soc. 79(2), 249–254 (1980) Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Cambridge University Press, Cambridge (1995) Denk, R., Hieber, M., Prüss, J.: \(R\)-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type, vol. 166, no. 788. Memoirs of the American Mathematical Society (2003) Eroglu, A., Omarova, M., Muradova, Sh.: Elliptic equations with measurable coefficients in generalized weighted Morrey spaces. In: Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences Azerbaijan, vol. 43, number (2), pp. 197–213 (2017) Foss, M., Passarelli di Napoli, A., Verde, A.: Global Morrey regularity results for asymptotically convex variational problems. Forum Math. 20(5), 921–953 (2008) Garcia-Cuerva, J., Rubio De Francia, J.L.: Weighted Norm Inequalities and Related Topics, North-Holland Mathematical Studies, vol. 116. North-Holland Publishing Co., Amsterdam (1985) Guliyev, V.S.: Generalized weighted Morrey spaces and higher order commutators of sublinear operators. Eurasian Math. J. 3(3), 33–61 (2012) Guliyev, V.S., Muradova, Sh., Omarova, M., Softova, L.: Gradient estimates for parabolic equations in generalized weighted Morrey spaces. Acta Math. Sin. 32(8), 911–924 (2016) Guliyev, V., Omarova, M., Sawano, Y.: Boundedness of intrinsec square functions and their commutators on generalized weighted Orlicz–Morrey spaces. Banach J. Math. Anal. 9(2), 44–62 (2015) Haller, R., Heck, H., Noll, A.: Mikhlin’s theorem for operator-valued Fourier multipliers in \(n\) variables. Math. Nachr. 244, 110–130 (2002) Ho, K.-P.: The fractional integral operators on Morrey spaces with variable exponent domains. Math. Inequal. Appl. 16(2), 363–373 (2013) Krein, S.G.: Linear Differential Equations in Banach Space, Translations of Mathematical Monographs, vol. 29. American Mathematical Society, Providence (1971) Kree, P.: Sur les multiplicateurs dans \({\cal{F}} \, L^{p} \) avec poids. Ann. Inst. Fourier 16, 91–121 (1966) Lions, J.-L., Peetre, J.: Sur une classe d’espaces d’interpolation. Inst. Hautes Etudes Sci. Publ. Math. 19, 5–68 (1964) Lizorkin, P.I.: \(\left( L_{p}, L_{q}\right)\)-multipliers of Fourier integrals. Dokl. Akad. Nauk. SSSR 152, 808–811 (1963) Lu, S., Shi, S.: A characterization of Campanato space via commutator of fractional integral. J. Math. Anal. Appl. 419(1), 123–137 (2014) McConnell, Terry R.: On Fourier multiplier transformations of Banach-valued functions. Trans. Am. Mater. Soc. 285(2), 739–757 (1984) Muckenhoupt, B.: Hardy’s inequality with weights, Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity I. Studia Math. 44, 31–38 (1972) Nakamura, S.: Generalized weighted Morrey spaces and classical operators. Math. Nachr. 289(17–18), 2235–2262 (2016) Pisier, G.: Some results on Banach spaces without local unconditional structure. Compos. Math. 37(1), 3–19 (1978) Ragusa, M.A.: Commutators of fractional integral operators on vanishing-Morrey spaces. J. Glob. Optim. 40(1–3), 361–368 (2008) Ragusa, M.A.: Homogeneous Herz spaces and regularity results. Nonlinear Anal. 71(12), e1909–e1914 (2009) Ragusa, M.A.: Embeddings for Morrey–Lorentz spaces. J. Optim. Theory Appl. 154(2), 491–499 (2012) Ragusa, M.A., Tachikawa, A., Takabayashi, H.: Partial regularity for \(p(x)\)-harmonic maps. Trans. AMS 365, 3329–3353 (2013) Shklyar, AYa.: Complete Second Order Linear Differential Equations in Hilbert Spaces, Operator Theory: Advances and Applications, vol. 92. Birkhauser, Basel (1997) Shakhmurov, V.B.: Embedding and maximal regular differential operators in Sobolev–Lions spaces. Acta Math. Sin. 22(5), 1493–1508 (2006) Shakhmurov, V.B.: Imbedding theorems and their applications to degenerate equations. Differ. Equ. 24(4), 475–482 (1988) Shakhmurov, V.B.: Coercive boundary value problems for strongly degenerating abstract equations. Dokl. Akad. Nauk. SSSR 290(3), 553–556 (1986) Shakhmurov, V.B.: Embedding operators and maximal regular differential-operator equations in Banach-valued function spaces. J. Inequal. Appl. 4, 329–345 (2005) Sobolev, S.L.: Some Applications of Functional Analysis in Mathematical Physics, Translations of Mathematical Monographs, vol. 90. American Mathematical Society, Providence (1991) Tanaka, H.: Morrey spaces and fractional operators. J. Aust. Math. Soc. 88(2), 247–259 (2010) Triebel, H.: Spaces of distributions with weights. Multipliers in \(L_{p} \)-spaces with weights. Math. Nachr. 78, 339–356 (1977) Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators, North-Holland Mathematical Library, vol. 18. North-Holland Publishing Co., Amsterdam (1978) Weis, L.: Operator-valued Fourier multiplier theorems and maximal \(L_{p}\) regularity. Math. Ann. 319(4), 735–758 (2001) Yakubov, S., Yakubov, Ya.: Differential-Operator Equations. Ordinary and Partial Differential Equations, Chapman and Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, vol. 103. Chapman and Hall/CRC, Boca Raton (2000) Zimmerman, F.: On vector-valued Fourier multiplier theorems. Studia Math. 93(3), 201–222 (1989)