Related papers: Weighted monotonicity inequalities for unbounded o…

In this paper, the new weighted inequalities were derived by-distance which is similar to the given inequality for the potential operator defined in [1].

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn by the author due to an error in the derivation.

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the author due to a crucial error in last part of proof.

This paper has been withdrawn by the author due to serious error found in main argument.

The paper has been withdrawn by the author due to crucial error in formula (14) which does not satisfy conditions for S(x,y) domain if only d>2.

This paper has been withdrawn by the author.

The paper has been withdrawn by the author.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author

This paper is withdrawn from submission due to a critical error in the proof of main theorem.

The paper has been withdrawn

This paper has been withdrawn by the author due to the incorrect argument for the security.

This article has been withdrawn due to an error in a proof of the main result.

This paper has been withdrawn by the author due to a crucial error in equation (51).

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.

This paper has been withdrawn by the author for further investigation.

This paper has been withdrawn by the author because there are some typos in proofs.