Results 1 to 10 of about 1,549 (180)
On Landau-Kolmogorov type inequalities for charges and their applications
Researches in Mathematics, 2023 In this article we prove sharp Landau-Kolmogorov type inequalities on a class of charges defined on Lebesgue measurable subsets of a cone in $\mathbb{R}^d$, $d\geqslant 1$, that are absolutely continuous with respect to the Lebesgue measure.
V.F. Babenko +3 more
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Kolmogorov-type inequalities for hypersingular integrals with homogeneous characteristics
Researches in MathematicsIn this article we obtain sharp Kolmogorov-type inequalities that estimate the uniform norm of a hypersingular integral operator $$ D^{w,\Omega}_K f(x): = \int_{C} w(|t|_K) (f(x+t) - f(x))\Omega(t)dt, x\in C, $$ using the uniform norm of the ...
V.F. Babenko +2 more
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Weighted Hardy’s inequalities and Kolmogorov-type operators [PDF]
Applicable Analysis, 2017 We give general conditions to state the weighted Hardy inequality \[ c\int_{\mathbb{R}^N}\frac{φ^2} {|x|^2}dμ\leq\int_{\mathbb{R}^N}|\nabla φ|^2 dμ+C\int_{\mathbb{R}^N} φ^2dμ,\quad φ\in C_c^{\infty}(\mathbb{R}^N),\,c\leq c_{0,μ}, \] with respect to a probability measure $dμ$. Moreover, the optimality of the constant $c_{0,μ}$ is given.
CANALE, Anna +3 more
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Some global Sobolev inequalities related to Kolmogorov-type operators
Bruno Pini Mathematical Analysis Seminar, 2020 In this note we review a recent result in [17] in collaboration with N. Garofalo, where we establish global versions of Hardy-Littlewood-Sobolev inequalities attached to hypoelliptic equations of Kolmogorov type.
Giulio Tralli
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Bi-Kolmogorov type operators and weighted Rellich’s inequalities [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2022 AbstractIn this paper we consider the symmetric Kolmogorov operator $$L=\Delta +\frac{\nabla \mu }{\mu }\cdot \nabla $$ L = Δ + ∇ μ
Davide Addona +3 more
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On an inequality of Kolmogorov type for a second-order difference expression
Journal of Inequalities and Applications, 1999 In this paper we discuss an inequality of Kolmogorov type for the square of a second-order formally symmetric difference expression in the limit point case.
Evans WD, Delil A
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Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic
Banach Journal of Mathematical Analysis, 2007 In this paper the authors establish new sharp Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic of multivariate functions from Hölder spaces. Applications of the results obtained to solve Stechkin's problem on the best approximation of unbounded hypersingular integral operator by unbounded ones on functional ...
Babenko, Vladislav F. +1 more
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Kolmogorov-type inequalities for functions with asymmetric restrictions on the highest derivative
Researches in MathematicsFor $k, r\in {\rm \bf N}$, $k0$; $\alpha, \beta>0$ and for functions $x\in L_{\infty}^r({\rm\bf R})$ inequalities that estimate the norm $\|x_{\pm }^{(k)}\|_{L_q[a,b]}$ on an arbitrary segment $[a,b] \subset {\rm\bf R}$ such that $\;x^{(k)}(a)=x^{(k)}(b)
V.A. Kofanov
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Improved Hardy Inequalities with a Class of Weights
Mathematics, 2023 In the framework of Hardy type inequalities and their applications to evolution problems, the paper deals with local and nonlocal weighted improved Hardy inequalities related to the study of Kolmogorov operators perturbed by singular potentials.
Anna Canale
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Kolmogorov inequalities for norms of Marchaud-type fractional derivatives of multivariate functions
Researches in Mathematics, 2020 We obtain new sharp Kolmogorov type inequalities, estimating the norm of mixed Marchaud type derivative of multivariate function through the C-norm of function itself and its norms in Hölder spaces.
N.V. Parfinovych, V.V. Pylypenko
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