Theory of Orlicz spaces by M.M. Rao, Z.D. Ren

By M.M. Rao, Z.D. Ren

A reference/text for mathematicians or scholars enthusiastic about research, differential equations, likelihood idea, and the learn of indispensable operators the place purely Lebesgue areas have been utilized in the earlier. Updates and extends the pioneering paintings through Krasnosel'skii and Rutickii of their 1958 treatise on Orl

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Fan, S. Lu, D. Yang, Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients, Georgian Math. J. 5 (1998) 425–440. [18] D. Gilbarg, N. , SpringerVerlag, Berlin, 1983. [19] A. Hinz, H. Kalf, Subsolution estimates and Harnack’s inequality for Schrödinger operators, J. Reine Angew. Math. 404 (1990) 118–131. [20] F. John, L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 4 (1961) 415–426. [21] D. Kim, N. Krylov, Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others, SIAM J.

For this purpose, we need the following well-known lemma. 1. ) Let 1 < p < ∞. Then (i) A function u belongs to W 1,p (Rn+ ) if and only if its even extension u with respect to x1 belongs to W 1,p (Rn+ ). Moreover, there exists C = C(n) > 0 such that 124 G. Pan, L. Tang / Journal of Functional Analysis 270 (2016) 88–133 C −1 u C −1 Du Lp (Rn +) Lp (Rn +) ≤ u Lp (Rn +) ≤ Du ≤C u Lp (Rn +) , Lp (Rn +) ≤ C Du . 6) (ii) A function u belongs to W 1,p (Rn+ ) and vanishes on ∂Rn+ if and only if its odd extension u with respect to x belongs to W 1,p (Rn+ ).

Fan, S. Lu, D. Yang, Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients, Georgian Math. J. 5 (1998) 425–440. [18] D. Gilbarg, N. , SpringerVerlag, Berlin, 1983. [19] A. Hinz, H. Kalf, Subsolution estimates and Harnack’s inequality for Schrödinger operators, J. Reine Angew. Math. 404 (1990) 118–131. [20] F. John, L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 4 (1961) 415–426. [21] D. Kim, N. Krylov, Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others, SIAM J.

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