Syarat Cukup Ketaksamaan Holder di Ruang Lebesgue dengan Variabel Eksponen

Mohamad Abdul Ba'is, Hairur Rahman, Erna Herawati

Abstract


Hӧlder inequality is a basic inequality in functional analysis. The inequality used for proofing other inequalities. In this research, the development of the application of the Hӧlder inequality in the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent. The integral Hӧlder inequality is used because the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent is a function space.This research shows the sufficient condition of Hӧlder inequality in Lebesgue spaces with variable exponent and the Morrey spaces with variable exponent according to the norm of the function and its characteristics.


Keywords


Hӧlder Inequality; Lebesgue Spaces with Variable Exponent; Morrey Spaces with Variable Exponent; Sufficient Condition

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References


S. Krantz, An Episodic History of Mathematics, Louis: h.iii, 2006.

O. K. d. J. Rakosnik, “On Space L^p(x) and W^k,p(x),” Czechoslovak Math, vol. 41, no. (116), p. 592–618, 1991.

X. d. T. S. Shao, “Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces,” Hindawi, vol. 2, no. 1, pp. 1-11, 2019.

C. Morrey, “On the solutions of quasi-linear elliptic partial differential equations,,” Transactions of the American Mathematical Society, vol. 43, no. 2, p. 126–166, 1938.

X. G. d. Z. J. Y. Li, “The Weighted Arithmetic Mean-Geometric Mean Inequality is Equivalent to the Holder Inequality,” Symmetry,, p. 10, 2018.

I. M. A. A. d. G. H. Ifronika, “ Generalized Holder’s Inequality in Morrey Spaces,” Matematicki Vesnik, vol. 4, no. 70, p. 326–337, 2018.

R. M. McLeod, K. Ranson dan L. Biehl, The generalized Riemann integral, JSTOR, 1980.

C. Godsil dan G. F. Royle, Algebraic graph theory, vol. 207, Springer Science & Business Media, 2013.

A. Gara, M. A. Blumrich, D. Chen, G.-T. Chiu, P. Coteus, M. E. Giampapa, R. A. Haring, P. Heidelberger, D. Hoenicke, G. V. Kopcsay dan others, “Overview of the Blue Gene/L system architecture,” IBM Journal of Research and Development, vol. 49, no. 2, pp. 195-212, 2005.

J. France, J. H. Thornley dan others, Mathematical models in agriculture., Butterworths, 1984.

F. E. Browder, “Nonexpansive nonlinear operators in a Banach space,” Proceedings of the National Academy of Sciences, vol. 54, no. 4, pp. 1041-1044, 1965.

M. J. Berger dan J. Oliger, “Adaptive mesh refinement for hyperbolic partial differential equations,” Journal of computational Physics, vol. 53, no. 3, pp. 484-512, 1984.




DOI: https://doi.org/10.18860/jrmm.v2i1.14619

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