Paper's Title:

Weak Type Inequalities for Some Operators on Generalized Morrey Spaces Over Metric Measure Spaces

Author(s):

Idha Sihwaningrum, Ari Wardayani, Hendra Gunawan

Faculty of Mathematics and Natural Sciences,
Jenderal Soedirman University, Purwokerto 53122,
Indonesia.
E-mail: idha.sihwaningrum@unsoed.ac.id ariwardayani@yahoo.co.id

Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
E-mail: hgunawan@math.itb.ac.id
URL: http://personal.fmipa.itb.ac.id/hgunawan/

Abstract:

We discuss weak type inequalities for maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces. Here the measure satisfies the so called growth condition. By taking into account the maximal operator, we obtain a Hedberg type inequality, which leads us to the weak type inequality for the fractional integral operator on the same spaces.

Paper's Title:

Some Inequalities for the Generalized Riesz Potential on the Generalized Morrey Spaces over Hypergroups

Author(s):

I. Sihwaningrum, Renny, Y. Dasril

Jenderal Soedirman University,
Indonesia.
E-mail: idha.sihwaningrum@unsoed.ac.id renny@unsoed.ac.id
 

Universiti Tun Hussein Onn,
Malaysia.
E-mail: yosza@uthm.edu.my

Abstract:

We present in this paper some inequalities for the generalized Riesz potential on the generalized Morrey spaces over commutative hypergroups. The results can be found by employing the maximal operator.

Paper's Title:

Banach-Saks Property and the Degree of Nondensifiability

Author(s):

Olivier de La Grandville

Departamento de Matemáticas,
Universidad Nacional de Educación a Distancia (UNED),
CL. Candalix s/n, 03202 Elche, Alicante,
Spain.
E-mail: gonzalogarciamacias@gmail.com

Abstract:

We present new upper bounds based on the so-called degree of nondensifiability (DND), for some quantification (see the references and definitions in the paper) of the Banach--Saks property. To be more precise, we prove that the mentioned quantification of a bounded subset of a Banach space can be bounded above by the DND of the convex hull of such a subset, multiplied by a constant. As a consequence of our main result, we derive an upper bound for the Banach-Saks property of bounded linear operators between Banach spaces. Through several examples, we show that such bounds are the best possible.

Paper's Title:

A_p Functions and Maximal Operator

Author(s):

Chunping Xie

Department of Mathematics,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
U. S. A.

E-mail: xie@msoe.edu

URL: http://www.msoe.edu/people/chunping.xie

Abstract:

The relationship between A_p functions and Hardy-Littlewood maximal operator on L^p,λ(w), the weighted Morrey space, has been studied. Also the extropolation theorem of L^p,λ(w) has been considered.

Paper's Title:

On the Constant in a Transference Inequality for the Vector-valued Fourier Transform

Author(s):

Dion Gijswijt and Jan van Neerven

Delft University of Technology,
Faculty EEMCS/DIAM,
 P.O. Box 5031,
2600 GA Delft,
The Netherlands.

URL: http://aw.twi.tudelft.nl/~neerven/
URL: http://homepage.tudelft.nl/64a8q/

E-mail: J.M.A.M.vanNeerven@TUDelft.nl
E-mail: D.C.Gijswijt@TUDelft.nl

Abstract:

The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.

Paper's Title:

Weyl's theorem for class Q and k - quasi class Q Operators

Author(s):

S. Parvatham and D. Senthilkumar

Department of Mathematics and Humanities,
Sri Ramakrishna Institute of Technology, Coimbatore-10, Tamilnadu,
India.
E-mail: parvathasathish@gmail.com

Post Graduate and Research Department of Mathematics,
Govt. Arts College, Coimbatore-641018, Tamilnadu,
India.
E-mail: senthilsenkumhari@gmail.com

Abstract:

In this paper, we give some properties of class  Q  operators. It is proved that every class  Q  operators satisfies Weyl's theorem under the condition that  T²  is isometry. Also we proved that every  k  quasi class  Q  operators is Polaroid and the spectral mapping theorem holds for this class of operator. It will be proved that single valued extension property, Weyl and generalized Weyl's theorem holds for every  k  quasi class  Q  operators.

Paper's Title:

Walrasian Equilibrium for Set-valued Mapping

Author(s):

M. Muslikh, R.B.E Wibowo, S. Fitri

Department of Mathematics,
University of Brawijaya,
Malang,
Indonesia.
E-mail: mslk@ub.ac.id
rbagus@ub.ac.id
saadatul@ub.ac.id

Abstract:

In this article, we obtain the existence of Walras equilibrium for set-valued demand mappings in a pure exchange economy. In this case, the set-valued mappings are defined by the loss function. Therefore, we shall summarize the features describing the exchange economy system which contain the loss function.

Paper's Title:

Inequalities Involving A_∞ Weights by Extrapolations

Author(s):

Chunping Xie

Mathematics Department,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
U.S.A.
E-mail: xie@msoe.edu
URL: https://www.msoe.edu/directory/profile/chunping.xie/

Abstract:

We generalize the extrapolation theorem from A_p weights to A_∞ weights on the setting of weighted Morrey spaces by using the Rubio de Francia algorithm and ideas in a paper by D. Cruz-Uribe et al. First we have proved the classical Hardy-Littlewood maximal operator is bounded on the weighted Morrey spaces if the weight w(x) is in A_∞ and then we have obtained inequalities involving the maximal operator, vector-valued maximal operator, the sharp maximal operator, and A_∞ weights.

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