Papers by Victor Burenkov
Complex Variables and Elliptic Equations, 2019
We introduce a class of Morrey-type spaces M λ p,q, , which includes the classical Morrey spaces ... more We introduce a class of Morrey-type spaces M λ p,q, , which includes the classical Morrey spaces and discuss their properties. We prove a Marcinkiewicz-type interpolation theorem for such spaces. This theorem is then applied to obtaining an analogue of O'Neil's inequality for convolutions and to proving the boundedness in the introduced Morrey-type spaces of the Riesz potential and singular integral operators.
Trace theorems
TEUBNER-TEXTE zur Mathematik, 1998
Best constants in reversed Hardy's inequalities for quasimonotonous functions
Prepr./Dep. of math. Chalmers univ. …, 1991
Inequalities for entire functions of exponential type satisfying % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9qqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbb...
Acta Mathematica Hungarica, 2007
ABSTRACT Let f be an entire function of exponential type satisfying the condition $ f(z) \equiv e... more ABSTRACT Let f be an entire function of exponential type satisfying the condition $ f(z) \equiv e^{i\gamma } e^{i\tau z} \overline {f(\bar z)} $ for some real γ. Lower and upper estimates for ∫ −∞∞|f′(x)|p dx in terms of ∫ −∞∞|f(x)|p dx, for such a function f belonging to L p (R), have been known in the case where p ∊ [1, ∞) and γ = 0. In this paper, these estimates are shown to hold for any p ∊ (0, ∞) and any real γ.
Conditional Hypoellipticity and Fourier Multipliers for Weighted L p -Spaces with an Exponential Weight
Teubner-Texte zur Mathematik, 1993
Our intention is to discuss some results, connected with a notion of conditional hypoellipticity,... more Our intention is to discuss some results, connected with a notion of conditional hypoellipticity, i.e. hypoellipticity in dependence on behaviour of solutions at infinity.
Second order Opial inequalities in ℒ p spaces and applications
Professor O. V. Besov honorary member of ISAAC
On the approximation of functions in the space W p r (Ω) by functions with compact support for an arbitrary open set Ω
Proceedings of the Steklov Institute of Mathematics
A two-sided estimate of the minimal norm of the extension operator for Sobolev spaces
Doklady Mathematics
The interaction of analysis and geometry. International school-conference on analysis and geometry, Novosibirsk, Russia, August 23–September 3, 2004
On an extremal property of quadrilaterals in an Aleksandrov space of curvature $\leq K$ by I. D. ... more On an extremal property of quadrilaterals in an Aleksandrov space of curvature $\leq K$ by I. D. Berg and I. G. Nikolaev On boundedness of the fractional maximal operator from complementary Morrey-type spaces to Morrey-type spaces by V. I. Burenkov, H. V. Guliyev, and V. S. Guliyev Generalized condensers and distortion theorems for conformal mappings of planar domains by V. N. Dubinin and D. B. Karp Rearrangement invariant envelopes of generalized Besov, Sobolev, and Calderon spaces by M. L. Goldman Null Lagrangians, the art of integration by parts by T. Iwaniec Geometric measure theory formulas on rectifiable metric spaces by M. Karmanova Stability and regularity of solutions to elliptic systems of partial differential equations by A. P. Kopylov Removable singularities of differential forms and $A$-solutions by V. M. Miklyukov Various generalizations of the volume conjecture by H. Murakami Gradient Young measures and applications to optimal design by P. Pedregal Wavelets for the cochlea by H. M. Reimann Sobolev-type classes of mappings with values in metric spaces by Y. G. Reshetnyak Counterexamples to elliptic regularity and convex integration by L. Szekelyhidi, Jr. Geometry of Carnot-Caratheodory spaces and differentiability of mappings by S. K. Vodopyanov Foundations of the theory of mappings with bounded distortion on Carnot groups by S. K. Vodopyanov.
On estimates of convolutions in Nikol’skij-Besov spaces
Progress in analysis. Proceedings of the 8th congress of the International Society for Analysis, its Applications, and Computation (ISAAC), Moscow, Russia, August 22–27, 2011. Volume 2
Sobolev’s integral representation
TEUBNER-TEXTE zur Mathematik, 1998
Notation and basic inequalities
TEUBNER-TEXTE zur Mathematik, 1998
TEUBNER-TEXTE zur Mathematik, 1998
More than 100 publications. Fields of research: real and functional analysis, partial differentia... more More than 100 publications. Fields of research: real and functional analysis, partial differential equations, especially the theory of function spaces (Sobolev spaces, spaces with fractional order of smoothness) and applications. Gedruckt auf chlorirei gebleichtem Papier. Die Deutsche Bibliothek-CIP-Einheitsaufnahme Burenkov, Viktor 1.: Sobolev spaces on domains I Viktor I. Burenkov.
Exact Analogues of the Hardy Inequality for Differences in the Case of Related Weights
[No abstract available
Spectral stability of elliptic selfadjoint differential operators with Dirichlet and Neumann boundary conditions
ABSTRACT We present a general spectral stability theorem for nonnegative selfadjoint operators wi... more ABSTRACT We present a general spectral stability theorem for nonnegative selfadjoint operators with compact resolvents, which is based on the notion of a transition operator, and some appli-cations to the study of the dependence of the eigenvalues of uniformly elliptic operators upon domain perturbation. Copyright © 2006 V. I. Burenkov and P. D. Lamberti. This is an open access article dis-tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is prop-erly cited.
On estimates of Fourier transforms and convolutions in Nikol'skii-Besov spaces
Hardy-type inequality for 0< p< 1 and hypodecreasing functions
Description of interpolation spaces for general local Morrey-type spaces
ABSTRACT We consider the real interpolation method and prove that for general local Morrey-type s... more ABSTRACT We consider the real interpolation method and prove that for general local Morrey-type spaces, in the case when they have the same integrability parameter, the interpolation spaces are again general local Morrey-type spaces with appropriately chosen parameters.
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Papers by Victor Burenkov