On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

Ali Akbulut; Vagif Guliyev; Rza Mustafayev

Mathematica Bohemica (2012)

  • Volume: 137, Issue: 1, page 27-43
  • ISSN: 0862-7959

Abstract

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In the paper we find conditions on the pair ( ω 1 , ω 2 ) which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space ℳ p , ω 1 to another ℳ p , ω 2 , 1 < p < ∞ , and from the space ℳ 1 , ω 1 to the weak space W ℳ 1 , ω 2 . As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.

How to cite

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Akbulut, Ali, Guliyev, Vagif, and Mustafayev, Rza. "On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces." Mathematica Bohemica 137.1 (2012): 27-43. <http://eudml.org/doc/246373>.

@article{Akbulut2012,
abstract = {In the paper we find conditions on the pair $(\omega _1,\omega _2)$ which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space $\mathcal \{M\}_\{p,\omega _1\}$ to another $\mathcal \{M\}_\{p,\omega _2\}$, $1<p<\infty $, and from the space $\mathcal \{M\}_\{1,\omega _1\}$ to the weak space $W\mathcal \{M\}_\{1,\omega _2\}$. As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.},
author = {Akbulut, Ali, Guliyev, Vagif, Mustafayev, Rza},
journal = {Mathematica Bohemica},
keywords = {generalized Morrey space; maximal operator; Hardy operator; singular integral operator; generalized Morrey space; maximal operator; Hardy operator; singular integral operator},
language = {eng},
number = {1},
pages = {27-43},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces},
url = {http://eudml.org/doc/246373},
volume = {137},
year = {2012},
}

TY - JOUR
AU - Akbulut, Ali
AU - Guliyev, Vagif
AU - Mustafayev, Rza
TI - On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces
JO - Mathematica Bohemica
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 137
IS - 1
SP - 27
EP - 43
AB - In the paper we find conditions on the pair $(\omega _1,\omega _2)$ which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space $\mathcal {M}_{p,\omega _1}$ to another $\mathcal {M}_{p,\omega _2}$, $1<p<\infty $, and from the space $\mathcal {M}_{1,\omega _1}$ to the weak space $W\mathcal {M}_{1,\omega _2}$. As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.
LA - eng
KW - generalized Morrey space; maximal operator; Hardy operator; singular integral operator; generalized Morrey space; maximal operator; Hardy operator; singular integral operator
UR - http://eudml.org/doc/246373
ER -

References

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