Displaying similar documents to “A nonlocal singular perturbation problem with periodic well potential”

Sharp L log α L inequalities for conjugate functions

Matts Essén, Daniel F. Shea, Charles S. Stanton (2002)

Annales de l’institut Fourier

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We give a method for constructing functions φ and ψ for which H ( x , y ) = φ ( x ) - ψ ( y ) has a specified subharmonic minorant h ( x , y ) . By a theorem of B. Cole, this procedure establishes integral mean inequalities for conjugate functions. We apply this method to deduce sharp inequalities for conjugates of functions in the class L log α L , for - 1 ≤ α < ∞ . In particular, the case α = 1 yields an improvement of Pichorides’ form of Zygmund’s classical inequality for the conjugates of functions in L log L . We also apply the method to produce a new...

Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces

M. Brundin (2007)

Czechoslovak Mathematical Journal

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If the Poisson integral of the unit disc is replaced by its square root, it is known that normalized Poisson integrals of L p and weak L p boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning and the author, respectively. In this paper we characterize the approach regions for boundary functions in two general classes of Orlicz spaces. The first of these classes contains spaces L Φ having the property L ∞ ⊂ L Φ ⊂ L p , 1 ≤ p < ∞ . The second contains...

Solutions for Toda systems on Riemann surfaces

Jiayu Li, Yuxiang Li (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper we study the solutions of Toda systems on Riemann surface in the critical case, proving a sufficient condition for existence.