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HIGHER ORDER LP-DERIVATIVE, LP –CONTINUITY AND LP –BOUNDEDNESS OF COMPLEX VALUED FUNCTION
T. K. Garai1
Section:Survey Paper, Product Type: Isroset-Journal
Vol.6 ,
Issue.1 , pp.307-310, Feb-2019
CrossRef-DOI: https://doi.org/10.26438/ijsrmss/v6i1.307310
Online published on Feb 28, 2019
Copyright © T. K. Garai . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: T. K. Garai, “HIGHER ORDER LP-DERIVATIVE, LP –CONTINUITY AND LP –BOUNDEDNESS OF COMPLEX VALUED FUNCTION,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.307-310, 2019.
MLA Style Citation: T. K. Garai "HIGHER ORDER LP-DERIVATIVE, LP –CONTINUITY AND LP –BOUNDEDNESS OF COMPLEX VALUED FUNCTION." International Journal of Scientific Research in Mathematical and Statistical Sciences 6.1 (2019): 307-310.
APA Style Citation: T. K. Garai, (2019). HIGHER ORDER LP-DERIVATIVE, LP –CONTINUITY AND LP –BOUNDEDNESS OF COMPLEX VALUED FUNCTION. International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(1), 307-310.
BibTex Style Citation:
@article{Garai_2019,
author = {T. K. Garai},
title = {HIGHER ORDER LP-DERIVATIVE, LP –CONTINUITY AND LP –BOUNDEDNESS OF COMPLEX VALUED FUNCTION},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {2 2019},
volume = {6},
Issue = {1},
month = {2},
year = {2019},
issn = {2347-2693},
pages = {307-310},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1187},
doi = {https://doi.org/10.26438/ijcse/v6i1.307310}
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v6i1.307310}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1187
TI - HIGHER ORDER LP-DERIVATIVE, LP –CONTINUITY AND LP –BOUNDEDNESS OF COMPLEX VALUED FUNCTION
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - T. K. Garai
PY - 2019
DA - 2019/02/28
PB - IJCSE, Indore, INDIA
SP - 307-310
IS - 1
VL - 6
SN - 2347-2693
ER -
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Abstract :
Higher order Lp-derivative of Complex valued functions is defined. It is shown that this derivative is more general than ordinary derivative. Also Lp-Continuity and Lp-boundedness is studied for these type of functions and it is proved that LP-continuity and LP-boundedness are more general than the ordinary continuity and ordinary boundedness.
Key-Words / Index Term :
Lp-derivative, Lp-Continuous, Lp-boundedness
References :
[1] A.P.Calderon and A.Zygmund, "Local Properties of Solutions of Elliptic partial differential equations", Studia Math, 20(1961), 171-225.
[2] M.J.Evans, "Lp-derivatives and Approximate Peano Derivative", Trans.Am. Math.Soc, 165(1972), 381-388.
[3] S.N.Mukhopadhyay, "Higher Order Derivative", Chapman and Hall/CRC, Monographs and Surveys in Pure and Applied Mathematics, 144(2012)
[4] A.Zygmund,"Trignometric Series ". Volume-1, Cambridge University Press, 1959.
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