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Displaying similar documents to “Some notes on embedding for anisotropic Sobolev spaces”

Some remarks on a class of weight functions

Loredana Caso, Maria Transirico (1996)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we obtain some results about a class of functions ρ : Ω R + , where Ω is an open set of R n , which are related to the distance function from a fixed subset S ρ Ω . We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function ρ .

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

Vagif Sabir Guliyev, Turhan Karaman, Rza Chingiz Mustafayev, Ayhan Şerbetçi (2014)

Czechoslovak Mathematical Journal

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In this paper, the boundedness of a large class of sublinear commutator operators T b generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces M p , ϕ ( w ) with the weight function w belonging to Muckenhoupt’s class A p is studied. When 1 < p < and b BMO , sufficient conditions on the pair ( ϕ 1 , ϕ 2 ) which ensure the boundedness of the operator T b from M p , ϕ 1 ( w ) to M p , ϕ 2 ( w ) are found. In all cases the conditions for the boundedness of T b are given in terms of Zygmund-type integral inequalities on ( ϕ 1 , ϕ 2 ) , which...

On optimal L p regularity in evolution equations

Alessandra Lunardi (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Using interpolation techniques we prove an optimal regularity theorem for the convolution u t = 0 t T t - s f s d s , where T t is a strongly continuous semigroup in general Banach space. In the case of abstract parabolic problems – that is, when T t is an analytic semigroup – it lets us recover in a unified way previous regularity results. It may be applied also to some non analytic semigroups, such as the realization of the Ornstein-Uhlenbeck semigroup in L p R n , 1 < p < , in which case it yields new optimal regularity results...