2017/05/22 by Veli Shakhmurov, Shakhmurov, Veli, Rishad Shahmurov +1
Mathematics · #34G10 #35J25 #35J70 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.1706.00812
openalex publication_date 2017/05/22 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28
The operator-valued multiplier theorems in weighted abstract Besov spaces are\nstudied. These results permit us to show embedding theorems in weighted\nBesov-Lions type spaces. The most regular class of interpolation space is found\nsuch that the mixed differential operator is bounded from Besov-Lions space to\nthis and Ehrling-Nirenberg-Gagliardo type sharp estimates are established. By\nusing these results the separability properties of degenerate differential\noperators are studied. Especially, we prove that the associated differential\noperators are positive and also are generators of analytic semigroups.\nMoreover, regularity properties for abstract elliptic equation, Cauchy problem\nfor degenerate abstract parabolic equation and the infinite systems of\ndegenerate parabolic equations are studied.\n