Grand Morrey type spaces

Grand Morrey type spaces

Автор: Samko Stefan G., Umarkhadzhiev Salaudin M.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 4 т.22, 2020 года.

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The so called grand spaces nowadays are one of the main objects in the theory of function spaces. Grand Lebesgue spaces were introduced by T. Iwaniec and C. Sbordone in the case of sets Ω with finite measure |Ω|

Morrey type space, grand space, grand morrey type space, grandizer, partial grandization, mixed grandization, homogeneous kernel, hardy type operator, hilbert operator

Короткий адрес: https://sciup.org/143172460

IDR: 143172460   |   DOI: 10.46698/c3825-5071-7579-i

Список литературы Grand Morrey type spaces

  • Iwaniec, T. and Sbordone, C. On the Integrability of the Jacobian under Minimal Hypotheses, Archive for Rational Mechanics and Analysis, 1992, vol. 119, no. 2, pp. 129-143. DOI: 10.1007/BF00375119
  • Fiorenza, A., Gupta, B. and Jain, P. The Maximal Theorem in Weighted Grand Lebesgue Spaces, Studia Mathematica, 2008, vol. 188, no. 2, pp. 123-133. DOI: 10.4064/sm188-2-2
  • Greco, L., Iwaniec, T., and Sbordone, C. Inverting the p-Harmonic Operator, Manuscripta Mathematica, 1997, vol. 92, no. 1, pp. 249-258. DOI: 10.1007/BF02678192
  • Jain, P., Singh, A. P., Singh, M. and Stepanov, V. Sawyer's Duality Principle for Grand Lebesgue Spaces, Mathematische Nachrichten, 2018, vol. 292, no. 4, pp. 841-849. DOI: 10.1002/mana.201700312
  • Kokilashvili, V. and Meskhi, A. A Note on the Boundedness of the Hilbert Transform in Weighted Grand Lebesgue Spaces, Georgian Mathematical Journal, 2009, vol. 16, no. 3, pp. 547-551.
  • Samko, S. G. and Umarkhadzhiev, S. M. On Iwaniec-Sbordone Spaces on Sets which May Have Infinite Measure, Azerbaijan Journal of Mathematics, 2011, vol. 1, no. 1, pp. 67-84.
  • Samko, S. G. and Umarkhadzhiev, S. M. On Iwaniec-Sbordone Spaces on Sets which May Have Infinite Measure: Addendum, Azerbaijan Journal of Mathematics, 2011, vol. 1, no. 2, pp. 143-144.
  • Samko, S. G. and Umarkhadzhiev, S. M. Riesz Fractional Integrals in Grand Lebesgue Spaces on Rn, Fractional Calculus and Applied Analysis, 2016, vol. 19, no. 3, pp. 608-624.
  • DOI: 10.1515/fca-2016-0033
  • Samko, S. G. and Umarkhadzhiev, S. M. On Grand Lebesgue Spaces on Sets of Infinite Measure, Mathematische Nachrichten, 2017, vol. 290, no. 5-6, pp. 913-919.
  • DOI: 10.1002/mana.201600136
  • Umarkhadzhiev, S. M. Generalization of the Notion of Grand Lebesgue Space, Russian Mathematics, 2014, vol. 58, no. 4, pp. 35-43.
  • DOI: 10.3103/S1066369X14040057
  • Kokilashvili, V., Meskhi, A. and Rafeiro, H. Riesz Type Potential Operators in Generalized Grand Morrey Spaces, Georgian Mathematical Journal, 2013, vol. 20, no. 1, pp. 43-64.
  • DOI: 10.1515/gmj-2013-0009
  • Meskhi, A. Maximal Functions, Potentials and Singular Integrals in Grand Morrey Spaces, Complex Variables and Elliptic Equations, 2011, vol. 56, no. 10-11, pp. 1003-1019.
  • DOI: 10.1080/17476933.2010.534793
  • Rafeiro, H. A Note on Boundedness of Operators in Grand Grand Morrey Spaces, Advances in Harmonic Analysis and Operator Theory, eds. A. Almeida, L. Castro and F.-O. Speck, Basel, Springer, 2013, vol. 229, pp. 349-356.
  • DOI: 10.1007/978-3-0348-0516-2-19
  • Umarkhadzhiev, S. M. The boundedness of the Riesz Potential Operator from Generalized Grand Lebesgue Spaces to Generalized Grand Morrey Spaces, Operator Theory, Operator Algebras and Applications, Basel, Birkhauser-Springer, 2014, pp. 363-373.
  • DOI: 10.1007/978-3-0348-0816-3-22
  • Guliyev, V. Integral Operators on Function Spaces on Homogeneous Groups and on Domains in Rn, PhD Thesis, Doctor's Degree, Moscow, Steklov Math. Inst., 1994, 329 p. (in Russian).
  • Guliyev, V. Function Spaces, Integral Operators and Two Weighted Inequalities on Homogeneous Groups. Some Applications, Baku, 1999, 332 p. (in Russian).
  • Adams, D. R. Lectures on Lp-Potential Theory, Umea University Reports, 1981, no. 2.
  • Burenkov, V. I. and Guliyev, H. Necessary and Sufficientconditions for Boundedness of the Maximal Operator in Local Morrey-Type Spaces, Studia Mathematica, 2004, vol. 163, no. 2, pp. 157-176.
  • DOI: 10.4064/sm163-2-4
  • Gogatishvili, A. and Mustafayev, R. Dual Spaces of Local Morrey-Type Spaces, Czechoslovak Mathematical Journal, 2011, vol. 61, no. 3, pp. 609-622.
  • DOI: 10.1007/s10587-011-0034-x
  • Burenkov, V. I. Recent Progress in Studying the Boundedness of Classical Operators of Real Analysis in General Morrey-Type Spaces. I, Eurasian Mathematical Journal, 2012, vol. 3, no. 3, pp. 11-32.
  • Burenkov, V. I. Recent Progress in Studying the Boundedness of Classical Operators of Real Analysis in General Morrey-Type Spaces. II, Eurasian Mathematical Journal, 2013, vol. 4, no. 1, pp. 21-45.
  • Rafeiro, H., Samko, N. and Samko, S. Morrey-Campanato Spaces: an Overview, Operator Theory, Pseudo-Differential Equations, and Mathematical Physics, eds. Y. Karlovich, L. Rodino, B. Silbermann, and I. Spitkovsky, 2013, Basel, Springer, vol. 228, pp. 293-323.
  • DOI: 10.1007/978-3-0348-0537-7_15
  • Samko, N. G. Integral Operators Commuting with Dilations and Rotations in Generalized Morrey-Type Spaces, Mathematical Methods in the Applied Sciences, 2020, vol. 43, no. 16, pp. 9416-9434.
  • DOI: 10.1002/mma.6279
  • Umarkhadzhiev, S. M. Integral Operators with Homogeneous Kernels in Grand Lebesgue Spaces, Mathematical Notes, 2017, vol. 102, no. 5-6, pp. 710-721.
  • DOI: 10.1134/S0001434617110104
  • Kokilashvili, V. and Meskhi, A. Weighted Sobolev Inequality in Grand Mixed Norm Lebesgue Spaces, Positivity, 2020.
  • DOI: 10.1007/s11117-020-00764-8
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