NDLI: L$^{ p }$-Estimates for pseudo-differential operators on $${\mathbb{Z}^n}$$

Content Provider	Springer Nature Link
Author	Carlos Andres, Rodriguez Torija
Copyright Year	2011
Abstract	In this work we give sufficient conditions on the symbol of a pseudo-differential operator on $${\mathbb Z^n}$$ ensuring the L $^{ p }$-boundedness. We give a sufficient condition for (p, q)-boundedness where $${\frac{1}{p}+ \frac{1}{q} =1}$$ . A sufficient condition for the L $^{ p }$-boundedness, 1 ≤ p < ∞, for a pseudo-differential operator whose symbol has certain differentiability properties with respect to the Fourier variable is also given. Other results establish a explicit relation between the (p, q)-weak continuity and the (p, q)-boundedness of a pseudo-differential operator. Some necessary conditions for boundedness and compactness are also given at the end.
Starting Page	367
Ending Page	375
Page Count	9
File Format	PDF
ISSN	16629981
Journal	Journal of Pseudo-Differential Operators and Applications
Volume Number	2
Issue Number	3
e-ISSN	1662999X
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2011-06-14
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fourier series Pseudo-differential operators L$^{ p }$-boundedness L$^{ p }$-compactness Pseudodifferential operators Integral operators Integral transforms Operators on function spaces Applications of Mathematics Partial Differential Equations Functional Analysis Operator Theory Analysis Algebra
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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

L$^{ p }$-Estimates for pseudo-differential operators on $${\mathbb{Z}^n}$$