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Register a new userSchrodinger type operators on generalized Morrey spaces
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In this paper we introduce a class of generalized Morrey spaces associated with Schrodinger operator $L=-Delta+V$. Via a pointwise estimate, we obtain the boundedness of the operators $V^{beta_{2}}(-Delta+V)^{-beta_{1}}$ and their dual operators on these Morrey spaces.
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We obtain Calderon-Zygmund type estimates in generalized Morrey spaces for nonlinear equations of $p$-Laplacian type. Our result is obtained under minimal regularity assumptions both on the operator and on the domain. This result allows us to study asymptotically regular operators. As a byproduct, we obtain also generalized Holder regularity of the solutions under some minimal restrictions of the weight functions.
Let $mathcal{L}=-Delta+V$ be a Schr{o}dinger operator, where the nonnegative potential $V$ belongs to the reverse H{o}lder class $B_{q}$. By the aid of the subordinative formula, we estimate the regularities of the fractional heat semigroup, ${e^{-tmathcal{L}^{alpha}}}_{t>0},$ associated with $mathcal{L}$. As an application, we obtain the $BMO^{gamma}_{mathcal{L}}$-boundedness of the maximal function, and the Littlewood-Paley $g$-functions associated with $mathcal{L}$ via $T1$ theorem, respectively.
In this note, we study the boundedness of integral operators $I_{g}$ and $T_{g}$ on analytic Morrey spaces. Furthermore, the norm and essential norm of those operators are given.
In this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the outcome belongs to the scale of the so-called diamond spaces.
Let $displaystyle L = -frac{1}{w} , mathrm{div}(A , abla u) + mu$ be the generalized degenerate Schrodinger operator in $L^2_w(mathbb{R}^d)$ with $dge 3$ with suitable weight $w$ and measure $mu$. The main aim of this paper is threefold. First, we obtain an upper bound for the fundamental solution of the operator $L$. Secondly, we prove some estimates for the heat kernel of $L$ including an upper bound, the Holder continuity and a comparison estimate. Finally, we apply the results to study the maximal function characterization for the Hardy spaces associated to the critical function generated by the operator $L$.
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