Vladikavkazskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vladikavkaz. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vladikavkaz. Mat. Zh., 2017, Volume 19, Number 2, Pages 3–10 (Mi vmj611)  

$L_p-L_q$-estimates for generalized Riss potentials with oscillating

M. N. Gurova, V. A. Noginba

a Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
b Southern Federal University, Rostov-on-Don

Abstract: We consider a class of multidimensional potential-type operators whose kernels are oscillating at infinity. The characteristics of these operators are infinitely differentiable homogeneous functions. We describe convex sets in the $(1/p;1/q)$-plane for which these operators are bounded from $L_p$ into $L_q$ and indicate the domains where they are not bounded. In some cases we describe their $\mathcal{L}$-characteristics. To obtain these results we use a new method based on special representation of the symbols of multidimensional potential-type operators. To these representations of the symbols we apply the technique of Fourier-multipliers, which degenerate or have singularities on the unit sphere in $\mathbb{R}^n$.

Key words: potential-type operators, oscillating kernel, method of Fourier multipliers, $L_p-L_q$-estimates, $\mathcal L$-characteristic.

Full text: PDF file (252 kB)
References: PDF file   HTML file
UDC: 517.983.2
Received: 08.07.2016

Citation: M. N. Gurov, V. A. Nogin, “$L_p-L_q$-estimates for generalized Riss potentials with oscillating”, Vladikavkaz. Mat. Zh., 19:2 (2017), 3–10

Citation in format AMSBIB
\Bibitem{GurNog17}
\by M.~N.~Gurov, V.~A.~Nogin
\paper $L_p-L_q$-estimates for generalized Riss potentials with oscillating
\jour Vladikavkaz. Mat. Zh.
\yr 2017
\vol 19
\issue 2
\pages 3--10
\mathnet{http://mi.mathnet.ru/vmj611}


Linking options:
  • http://mi.mathnet.ru/eng/vmj611
  • http://mi.mathnet.ru/eng/vmj/v19/i2/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Владикавказский математический журнал
    Number of views:
    This page:134
    Full text:37
    References:19

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022