Inequalities for Green’s operator applied to the minimizers
نویسندگان
چکیده
* Correspondence: sding@seattleu. edu Department of Mathematics, Seattle University, Seattle, WA 98122, USA Full list of author information is available at the end of the article Abstract In this paper, we prove both the local and global L -norm inequalities for Green’s operator applied to minimizers for functionals defined on differential forms in L -averaging domains. Our results are extensions of L norm inequalities for Green’s operator and can be used to estimate the norms of other operators applied to differential forms. 2000 Mathematics Subject Classification: Primary: 35J60; Secondary 31B05, 58A10, 46E35.
منابع مشابه
Inequalities of Ando's Type for $n$-convex Functions
By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.
متن کاملSingular integrals of the compositions of Laplace- Beltrami and Green’s operators
* Correspondence: [email protected]. cn Department of Mathematics, Harbin Institute of Technology Harbin 150001, P.R.China Full list of author information is available at the end of the article Abstract We establish the Poincaré-type inequalities for the composition of the LaplaceBeltrami operator and the Green’s operator applied to the solutions of the nonhomogeneous A-harmonic equation in the Joh...
متن کاملFurther inequalities for operator space numerical radius on 2*2 operator matrices
We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$, when $X$ is a numerical radius operator space. These inequalities contain some upper and lower bounds for operator space numerical radius.
متن کاملA note on inequalities for Tsallis relative operator entropy
In this short note, we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy, {em Math. Inequal. Appl.} {18} (2015), no. 2, 401--406]. Meanwhile, we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...
متن کاملCoarse and Precise L-green Potential Estimates on Noncompact Riemannian Manifolds
Abstract. We are concerned about the coarse and precise aspects of a priori estimates for Green’s function of a regular domain for the Laplacian-Betrami operator on any 3 ≤ n-dimensional complete non-compact boundary-free Riemannian manifold through the square Sobolev/Nash/logarithmic-Sobolev inequalities plus the rough and sharp Euclidean isoperimetric inequalities. Consequently, we are led to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011