Some notes on embedding for anisotropic Sobolev spaces

Hongliang Li; Quinxiu Sun

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 $ρ : Ω \to R_{+}$ , where $Ω$ is an open set of $R^{n}$ , which are related to the distance function from a fixed subset $S_{ρ} \subset \partial Ω$ . 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 $1 < p < \infty$ and $b \in BMO$ , 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 boundedness of weighted Hardy operator in $L^{p (\cdot)}$ and regularity condition.

Harman, Aziz, Mamedov, Farman Imran (2010)

Journal of Inequalities and Applications [electronic only]

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A kind of estimate of difference norms in anisotropic weighted Sobolev-Lorentz spaces.

Chen, Jiecheng, Li, Hongliang (2009)

Journal of Inequalities and Applications [electronic only]

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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 $u (t) = \int_{0}^{t} T (t - s) f (s) d s$ , 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 $L^{p} (R^{n})$ , $1 < p < \infty$ , in which case it yields new optimal regularity results...

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

Some remarks on a class of weight functions

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

On boundedness of weighted Hardy operator in L p ( · ) and regularity condition.

A kind of estimate of difference norms in anisotropic weighted Sobolev-Lorentz spaces.

On optimal L p regularity in evolution equations

On boundedness of weighted Hardy operator in $L^{p (\cdot)}$ and regularity condition.

On optimal $L^{p}$ regularity in evolution equations