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Asekritova, Irina
Publications (10 of 28) Show all publications
Asekritova, I., Cerdá, J. & Kruglyak, N. (2012). The Riesz-Herz equivalence for capacitary maximal functions. Revista Matemática Complutense, 25(1), 43-59
Open this publication in new window or tab >>The Riesz-Herz equivalence for capacitary maximal functions
2012 (English)In: Revista Matemática Complutense, ISSN 1139-1138, Vol. 25, no 1, p. 43-59Article in journal (Refereed) Published
Abstract [en]

We prove a Riesz-Herz estimate for the maximal function associated toa capacity ConRn,MCf(x)=supQxC(Q)−1Q|f|, which extends the equivalence (Mf )∗(t)f∗∗(t) for the usual Hardy-Littlewood maximal function Mf. The proof is based on an extension of the Wiener-Stein estimates for the distribution function of the maximal function, obtained using a convenient family of dyadiccubes. As a byproduct we obtain a description of the norm of the interpolationspace (L1,L1,C)1/p,p,  where L1,C denotes the Morrey space based on a capacity.

Keywords
Maximal function, Capacity, Morrey space, Dyadic cubes, Interpolation spaces
National Category
Geometry
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-7631 (URN)10.1007/s13163-010-0057-0 (DOI)2-s2.0-84866413740 (Scopus ID)
Available from: 2010-08-22 Created: 2010-08-22 Last updated: 2016-03-11Bibliographically approved
Asekritova, I. & Kruglyak, N. (2010). The Besikovitch Covering Theorem and Near Minimizers for the Couple (L2,BV). Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, 59(1), 29-33
Open this publication in new window or tab >>The Besikovitch Covering Theorem and Near Minimizers for the Couple (L2,BV)
2010 (English)In: Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, ISSN 1406-0086, E-ISSN 2228-0685, Vol. 59, no 1, p. 29-33Article in journal (Refereed) Published
Keywords
real interpolation, Besicovitch Covering Theorem, near minimizers
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-7626 (URN)
Available from: 2010-08-22 Created: 2010-08-22 Last updated: 2017-12-12Bibliographically approved
Asekritova, I., Nilsson, B. & Rydström, S. (2009). Diffractive Index Determination by Tikhonov Regularization on Forced String Vibration Data. In: Mathematical modelling of wave phenomena: 3rd Conference on Mathematical Modelling of Wave Phenomena, Växjö, Sweden, 9-13 June 2008. Paper presented at 3rd Conference on Mathematical Modelling of Wave Phenomena, Växjö, Sweden, 9-13 June 2008 (pp. 224-232). Melville, New York: American Institute of Physics
Open this publication in new window or tab >>Diffractive Index Determination by Tikhonov Regularization on Forced String Vibration Data
2009 (English)In: Mathematical modelling of wave phenomena: 3rd Conference on Mathematical Modelling of Wave Phenomena, Växjö, Sweden, 9-13 June 2008, Melville, New York: American Institute of Physics , 2009, p. 224-232Conference paper, Published paper (Refereed)
Abstract [en]

Wave analysis is efficient for investigating the interior of objects. Examples are ultra sound examination of humans and radar using elastic and electromagnetic waves. A common procedure is inverse scattering where both transmitters and receivers are located outside the object or on its boundary. A variant is when both transmitters and receivers are located on the scattering object. The canonical model is a finite inhomogeneous string driven by a harmonic point force. The inverse problem for the determination of the diffractive index of the string is studied. This study is a first step to the problem for the determination of the mechanical strength of wooden logs. An inverse scattering theory is formulated incorporating two regularizing strategies. The results of simulations using this theory show that the suggested method works quite well and that the regularization methods based on the couple of spaces (L2; H1 ) could be very useful in such problems.

 

 

Place, publisher, year, edition, pages
Melville, New York: American Institute of Physics, 2009
Series
AIP Conference Proceedings, ISSN 0094-243X ; 1106
Keywords
string vibrations, Tikhonov regularization, elastic properties, inverse problem
National Category
Computational Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:vxu:diva-7403 (URN)978-0-07354-0643-8 (ISBN)
Conference
3rd Conference on Mathematical Modelling of Wave Phenomena, Växjö, Sweden, 9-13 June 2008
Available from: 2009-03-23 Created: 2009-03-23 Last updated: 2013-08-22Bibliographically approved
Asekritova, I. (2008). Invertibility of Operators in Spaces of Real Interpolation. Revista Matematica Complutense, 21(1), 207-217
Open this publication in new window or tab >>Invertibility of Operators in Spaces of Real Interpolation
2008 (English)In: Revista Matematica Complutense, ISSN 1139-1138, Vol. 21, no 1, p. 207-217Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Madrid, 2008
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:vxu:diva-3933 (URN)
Available from: 2009-01-07 Created: 2009-01-07 Last updated: 2010-03-09Bibliographically approved
Asekritova, I. (2008). Regularization Theory and Real Interpolation.
Open this publication in new window or tab >>Regularization Theory and Real Interpolation
2008 (English)Conference paper, Published paper (Other (popular science, discussion, etc.))
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:vxu:diva-3936 (URN)
Available from: 2009-01-07 Created: 2009-01-07 Last updated: 2010-03-09Bibliographically approved
Asekritova, I. (2006). Interpolation of Approximation Spaces with Nonlinear Projectors. Proceedings of the Estonian Academy of Sciences, 55(3), 146-149
Open this publication in new window or tab >>Interpolation of Approximation Spaces with Nonlinear Projectors
2006 (English)In: Proceedings of the Estonian Academy of Sciences, ISSN 1406-0086, Vol. 55, no 3, p. 146-149Article in journal (Refereed) Published
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:vxu:diva-4311 (URN)
Available from: 2007-03-14 Created: 2007-03-14 Last updated: 2010-03-10Bibliographically approved
Asekritova, I. & Kruglyak, N. (2006). Interpolation of Besov and Sobolev Spaces in the Non-Diagonal Case. In: Constructive Theory of Functions: Proceedings of International Conference, Varna (pp. 45-50).
Open this publication in new window or tab >>Interpolation of Besov and Sobolev Spaces in the Non-Diagonal Case
2006 (English)In: Constructive Theory of Functions: Proceedings of International Conference, Varna, 2006, p. 45-50Conference paper, Published paper (Refereed)
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:vxu:diva-4312 (URN)954-322-144-8 (ISBN)
Available from: 2007-03-14 Created: 2007-03-14 Last updated: 2010-03-10Bibliographically approved
Asekritova, I. & Kruglyak, N. (2006). Interpolation of Besov Spaces in the Non-Diagonal Case. Algebra and Analysis, 18(4), 1-9
Open this publication in new window or tab >>Interpolation of Besov Spaces in the Non-Diagonal Case
2006 (English)In: Algebra and Analysis, ISSN 1061-0022, Vol. 18, no 4, p. 1-9Article in journal (Refereed) Published
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:vxu:diva-4310 (URN)
Available from: 2007-03-14 Created: 2007-03-14 Last updated: 2010-03-10Bibliographically approved
Asekritova, I., Kruglyak, N. & Nikolova, L. (2005). Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation. Studia Mathematica, 170(3), 227-239
Open this publication in new window or tab >>Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation
2005 (English)In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 170, no 3, p. 227-239Article in journal (Refereed) Published
Keywords
Real interpolation, Lizorkin-Freitag formula, vector-valued spaces
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-7645 (URN)
Available from: 2010-08-22 Created: 2010-08-22 Last updated: 2017-12-12Bibliographically approved
Asekritova, I. & Kruglyak, N. (2005). Real Interpolation of Vector-Valued Spaces in Non-Diagonal Case. Proceedings of the American Mathematical Society, 133(6), 1665-1675
Open this publication in new window or tab >>Real Interpolation of Vector-Valued Spaces in Non-Diagonal Case
2005 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 133, no 6, p. 1665-1675Article in journal (Refereed) Published
Keywords
interpolation, vector-valued spaces
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-7625 (URN)
Available from: 2010-08-22 Created: 2010-08-22 Last updated: 2017-12-12Bibliographically approved

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