Shakhmurov,V.Shahmurov,R.2024-05-252024-05-25201081331-434310.7153/mia-13-302-s2.0-77952594681https://doi.org/10.7153/mia-13-30https://hdl.handle.net/20.500.14517/2240In the present paper, separability properties of convolution-differential equations with unbounded operator coefficients in Banach valued Lp spaces are investigated. A coercive estimate for resolvent of corresponding realization operator, especially, its R-sectoriality is obtained. Finally, these results applied to establish maximal regularity of Cauchy problem for the abstract parabolic convolution equations and integro-differential equations on infinite dimension state spaces. © ELEMENT, Zagreb.eninfo:eu-repo/semantics/openAccessAbstract cauchy problemBanach-valued l_p spacesBoundary value problemsIntegro-differential equationsOperator-valued multipliersSectorial operatorsArticleQ2Q2132387404