Intrinsic square functions on functions spaces including weighted Morrey spaces

@article{Feuto2012IntrinsicSF,
  title={Intrinsic square functions on functions spaces including weighted Morrey spaces},
  author={Justin Feuto},
  journal={arXiv: Classical Analysis and ODEs},
  year={2012}
}
  • J. Feuto
  • Published 1 May 2012
  • Mathematics
  • arXiv: Classical Analysis and ODEs
We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^{\ast}_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered. 
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References

SHOWING 1-10 OF 21 REFERENCES
Intrinsic square functions on the weighted Morrey spaces
The intrinsic square function
We show that the Lusin area function and essentially all of its real-variable generalizations are pointwise dominated by an “intrinsic” square function, and that this latter function is, for all…
Weighted Morrey spaces and a singular integral operator
In this paper, we shall introduce a weighted Morrey space and study the several properties of classical operatorsin harmonic analysis on this space (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modern Fourier Analysis
Preface.- Smoothness and Function Spaces.- BMO and Carleson Measures.- Singular Integrals of Nonconvolution Type.- Weighted Inequalities.- Boundedness and Convergence of Fourier Integrals.-…
Regularity in Morrey Spaces of Strong Solutions to Nondivergence Elliptic Equations with VMO Coefficients
In this paper, by means of the theories of singular integrals and linear commutators, the authors establish the regularity in Morrey spaces of strong solutions to nondivergence elliptic equations…
Norms inequalities in some subspaces of Morrey space
We give norm inequalities for some classical operators in amalgams spaces and in some subspace of Morrey space.
INTEGRABLE FRACTIONAL MEAN FUNCTIONS ON SPACES OF HOMOGENEOUS TYPE.
The class of Banach spaces (L q , L p ) � (X, d, � ), 1 ≤ q ≤ α ≤ p ≤ ∞, introduced in (10) in connection with the study of the continuity of the fractional maximal operator of Hardy-Littlewood and…
Espaces de fonctions à moyenne fractionnaire intégrable sur les groupes localement compacts
Let $G$ be a locally compact group which is $\sigma $-compact, endowed with a left Haar measure $\lambda .$ Denote by $e$ the unit element of $G$, and by $B$ an open relatively compact and symmetric…
Weighted norm inequalities for the Hardy maximal function
The principal problem considered is the determination of all nonnegative functions, U(x), for which there is a constant, C, such that | [f*(x)rUix)dx g CJ \f(x)\'U(x) dx, where l<p<oo, J is a fixed…
Weighted Norm Inequalities for a Maximal Operator in Some Subspace of Amalgams
Abstract We give weighted norm inequalities for the maximal fractional operator ${{\mathcal{M}}_{q}},\beta $ of Hardy–Littlewood and the fractional integral ${{I}_{\gamma }}$ . These inequalities are…
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