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Lewy's example and most other allied examples of non-solvable operators have only complex coefficients. Leaving open the question of unsolvable operators with real coefficient. F.Treves in 1962 has constructed a fourth order operator iterating Lewy operator.

If $P$ is Lewy operator then $PP\bar{P}\bar{P}$ is a real coefficient fouth fourth order operator which is not local solvable.

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Lewy's example and most other allied examples of unsolvable non-solvable operators have only complex coefficients. Leaving open the question of unsolvable operators with real coefficient. F.Treves in 1962 has constructed a fourth order operator iterating Lewy operator.

If $P$ is Lewy operator then $PP\bar{P}\bar{P}$ is a real coefficient fouth order operator which is not local solvable.

If $P$ is Lewy operator then $PP\bar{P}\bar{P}$ is a real coefficient fouth order operator which is not local solvable.