$L^p$-boundedness of pseudo-differential operators on homogeneous trees

Pseudo-differential calculus on homogeneous trees

Abstract. In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol classes and associated operators. We prove that these operators are bounded on L and give adjoint and product formulas. Finally we compute the symb...

L^-BOUNDEDNESS OF PSEUDO-DIFFERENTIAL OPERATORS OF CLASS S0,o

We study the 7_/-boundedness of pseudo-differential operators with the support of their symbols being contained in ExR" , where E is a compact subset of R" , and their symbols have derivatives with respect to x only up to order k , in the Holder continuous sense, where k > n/2 (the case 1 < p < 2) and k > n/p (the case 2 < p < oo). We also give a new proof of the LPboundedness, 1 < p < oo , of ...

Boundedness Properties of Pseudo-differential Operators and Calderón-zygmund Operators on Modulation Spaces

In this paper, we study the boundedness of pseudo-differential operators with symbols in Sm ρ,δ on the modulation spaces M p,q. We discuss the order m for the boundedness Op(Sm ρ,δ) ⊂ L(M p,q(Rn)) to be true. We also prove the existence of a Calderón-Zygmund operator which is not bounded on the modulation space Mp,q with q 6= 2. This unboundedness is still true even if we assume a generalized T...

Maximal operator for pseudo-differential operators with homogeneous symbols

The aim of the present paper is to obtain a Sjölin-type maximal estimate for pseudo-differential operators with homogeneous symbols. The crux of the proof is to obtain a phase decomposition formula which does not involve the time traslation. The proof is somehow parallel to the paper by Pramanik and Terwilleger (P. Malabika and E. Terwilleger, A weak L2 estimate for a maximal dyadic sum operato...

Boundedness of Sublinear Operators on the Homogeneous Herz Spaces