NDLI: Weighted weak modular and norm inequalities for the Hardy operator in variable L $^{ p }$ spaces of monotone functions

Please wait, while we are loading the content...

Revista Matemática Complutense : Volume 30

Revista Matemática Complutense : Volume 29

Revista Matemática Complutense : Volume 28

Revista Matemática Complutense : Volume 27

Revista Matemática Complutense : Volume 26

Revista Matemática Complutense : Volume 25

Revista Matemática Complutense : Volume 25, Issue 2, July 2012

Semigroup estimates and stability/instability results for the linearized three waves interaction equations

On a general weighted Hardy type inequality in the variable exponent Lebesgue spaces

Simple Neumann eigenvalues for the Laplace operator in a domain with a small hole : A functional analytic approach

Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in ${\bf R}^{n}$

Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators

Weighted weak modular and norm inequalities for the Hardy operator in variable L $^{ p }$ spaces of monotone functions

Schur-Szegő composition of entire functions

Spatial graphs with local knots

Heegaard surfaces for certain graphs in compressionbodies

Some remarks on the planar Kouchnirenko’s theorem

Determination of the real poles of the Igusa zeta function for curves

Revista Matemática Complutense : Volume 25, Issue 1, January 2012

Revista Matemática Complutense : Volume 24

Revista Matemática Complutense : Volume 23

Weighted weak modular and norm inequalities for the Hardy operator in variable L $^{ p }$ spaces of monotone functions

Content Provider	Springer Nature Link
Author	Boza, Santiago Soria, Javier
Copyright Year	2011
Abstract	We study weak-type modular inequalities for the Hardy operator restricted to non-increasing functions on weighted L $^{ p(⋅)}$ spaces, where p(⋅) is a variable exponent. These new estimates complete the results of Boza and Soria (J. Math. Anal. Appl. 348:383–388, 2008) where we showed some necessary and sufficient conditions on the exponent p(⋅) and on the weights to obtain weighted modular inequalities with variable exponents. For this purpose, we introduced the class of weights B $_{ p(⋅)}$. We prove that, for exponents p(x)>1, this is also the class of weights for which the weak modular inequality holds, and a characterization is also given in the case p(x)≤1. Finally, we compare our theory with the results in Neugebauer (Stud. Math. 192(1):51–60, 2009), giving examples for very concrete and simple exponents which show that inequalities in norm hold true in a very general context.
Starting Page	459
Ending Page	474
Page Count	16
File Format	PDF
ISSN	11391138
Journal	Revista Matemática Complutense
Volume Number	25
Issue Number	2
e-ISSN	19882807
Language	English
Publisher	Springer Milan
Publisher Date	2011-05-18
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Modular inequalities Hardy operator B $_{ p }$ weights Variable L $^{ p }$ spaces Monotone functions Inequalities involving derivatives and differential and integral operators Spaces of measurable functions Topology Geometry Applications of Mathematics Analysis Mathematics Algebra
Content Type	Text
Resource Type	Article
Subject	Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Weighted estimates for the averaging integral operator

On a Hardy Type General Weighted Inequality in Spaces L p(·)

Optimal relationships between $$L^p$$ -norms for the Hardy operator and its dual

Inequalities for Riemann-Liouville operator involving suprema

On a general weighted Hardy type inequality in the variable exponent Lebesgue spaces

Multidimensional Hilbert-type Inequality on the Weighted Orlicz Spaces

Integral isoperimetric transference and dimensionless Sobolev inequalities

The rearrangement-invariant space $$\Gamma _{p,\phi }$$

$$M_{p}$$ weights for bilinear Hardy operators on $$\mathbb R ^{n}$$

Weighted weak modular and norm inequalities for the Hardy operator in variable L $^{ p }$ spaces of monotone functions

Similar Documents

Weighted estimates for the averaging integral operator

On a Hardy Type General Weighted Inequality in Spaces L p(·)

Optimal relationships between $$L^p$$ -norms for the Hardy operator and its dual

Inequalities for Riemann-Liouville operator involving suprema

On a general weighted Hardy type inequality in the variable exponent Lebesgue spaces

Multidimensional Hilbert-type Inequality on the Weighted Orlicz Spaces

Integral isoperimetric transference and dimensionless Sobolev inequalities

The rearrangement-invariant space $$\Gamma _{p,\phi }$$

$$M_{p}$$ weights for bilinear Hardy operators on $$\mathbb R ^{n}$$

Weighted weak modular and norm inequalities for the Hardy operator in variable L $^{ p }$ spaces of monotone functions