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We obtain Calderon-Zygmund type estimates in generalized Morrey spaces for nonlinear equations of $p$-Laplacian type. Our result is obtained under minimal regularity assumptions both on the operator and on the domain. This result allows us to study asymptotically regular operators. As a byproduct, we obtain also generalized Holder regularity of the solutions under some minimal restrictions of the weight functions.
In this paper we introduce a class of generalized Morrey spaces associated with Schrodinger operator $L=-Delta+V$. Via a pointwise estimate, we obtain the boundedness of the operators $V^{beta_{2}}(-Delta+V)^{-beta_{1}}$ and their dual operators on these Morrey spaces.
In this note, we study the boundedness of integral operators $I_{g}$ and $T_{g}$ on analytic Morrey spaces. Furthermore, the norm and essential norm of those operators are given.
We study ultradistributional boundary values of zero solutions of a hypoelliptic constant coefficient partial differential operator $P(D) = P(D_x, D_t)$ on $mathbb{R}^{d+1}$. Our work unifies and considerably extends various classical results of Koma
Let (X j , d j , $mu$ j), j = 0, 1,. .. , m be metric measure spaces. Given 0 < p $kappa$ $le$ $infty$ for $kappa$ = 1,. .. , m and an analytic family of multilinear operators T z : L p 1 (X 1) x $bullet$ $bullet$ $bullet$ L p m (X m) $rightarrow$ L
In this paper we consider second order parabolic partial differential equations subject to the Dirichlet boundary condition on smooth domains. We establish weighted $L_{q}$-maximal regularity in weighted Triebel-Lizorkin spaces for such parabolic pro