Boundedness Properties of Pseudo-differential Operators and Calderón-zygmund Operators on Modulation Spaces
نویسندگان
چکیده
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 (1) condition. These results are induced by the unboundedness of pseudo-differential operators on Mp,q whose symbols are of the class S 1,δ with 0 < δ < 1.
منابع مشابه
Bilinear Square Functions and Vector-Valued Calderón-Zygmund Operators
Boundedness results for bilinear square functions and vector-valued operators on products of Lebesgue, Sobolev, and other spaces of smooth functions are presented. Bilinear vector-valued Calderón-Zygmund operators are introduced and used to obtain bounds for the optimal range of estimates in target Lebesgue spaces including exponents smaller than one.
متن کاملMultilinear Calderón-zygmund Operators on Hardy Spaces
It is shown that multilinear Calderón-Zygmund operators are bounded on products of Hardy spaces.
متن کاملA Counterexample for Boundedness of Pseudo-differential Operators on Modulation Spaces
We prove that pseudo-differential operators with symbols in the class S 1,δ (0 < δ < 1) are not always bounded on the modulation space M (q 6= 2).
متن کاملBilinear Fourier integral operator and its boundedness
We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.
متن کاملSOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS
In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...
متن کامل