On inequalities of Kolmogorov type for the functions being analytic in the unit bicircle
The sharp inequality of Kolmogorov type has been obtained in the space $\mathfrak{B}(U_2)$ for functions of two complex variables analytic in the unit bicircle.
S.B. Vakarchuk, M.B. Vakarchuk
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Some global Sobolev inequalities related to Kolmogorov-type operators
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. The relevant Sobolev spaces are defined through the fractional powers of the operator under consideration.
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Kolmogorov-type inequalities for functions with asymmetric restrictions on the highest derivative
For $k, r\in {\rm \bf N}$, $k<r$; $q\ge 1$, $p>0$; $\alpha, \beta>0$ 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 $\;x^{(k)}(a)=x^{(k)}(b)=0$ via a local norm of the function $|||x^{\uparrow \downarrow}|||_p ...
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The Physics, Information, and Computation of Perennial Learning: Kolmogorov Complexity, Information Distance, and Port-Hamiltonian Thermodynamics. [PDF]
Bajaj C.
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Note on a "Kolmogorov-Type" Inequality
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On De Giorgi's conjecture of nonlocal approximations for free-discontinuity problems: The symmetric gradient case. [PDF]
Almi S, Davoli E, Kubin A, Tasso E.
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Kolmogorovian Censorship, Predictive Incompleteness, and the Locality Loophole in Bell Experiments. [PDF]
Grangier P.
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Cumulant-Based Approaches for Testing the Assumption of Independent Errors in Non-Gaussian Parallel and Congeneric Measures. [PDF]
Wiedermann W, Shi D.
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