diff --git a/test/test_arraycontext.py b/test/test_arraycontext.py
index 75a91cb5..6b3fd1dd 100644
--- a/test/test_arraycontext.py
+++ b/test/test_arraycontext.py
@@ -756,6 +756,59 @@ def test_container_scalar_map(actx_factory):
         assert result is not None
 
 
+def test_container_map(actx_factory):
+    actx = actx_factory()
+    ary_dof, ary_of_dofs, mat_of_dofs, dc_of_dofs, bcast_dc_of_dofs = \
+            _get_test_containers(actx)
+
+    # {{{ check
+
+    def _check_allclose(f, arg1, arg2, atol=2.0e-14):
+        from arraycontext import NotAnArrayContainerError
+        try:
+            arg1_iterable = serialize_container(arg1)
+            arg2_iterable = serialize_container(arg2)
+        except NotAnArrayContainerError:
+            assert np.linalg.norm(actx.to_numpy(f(arg1) - arg2)) < atol
+        else:
+            arg1_subarrays = [
+                subarray for _, subarray in arg1_iterable]
+            arg2_subarrays = [
+                subarray for _, subarray in arg2_iterable]
+            for subarray1, subarray2 in zip(arg1_subarrays, arg2_subarrays):
+                _check_allclose(f, subarray1, subarray2)
+
+    def func(x):
+        return x + 1
+
+    from arraycontext import rec_map_array_container
+    result = rec_map_array_container(func, 1)
+    assert result == 2
+
+    for ary in [ary_dof, ary_of_dofs, mat_of_dofs, dc_of_dofs]:
+        result = rec_map_array_container(func, ary)
+        _check_allclose(func, ary, result)
+
+    from arraycontext import mapped_over_array_containers
+
+    @mapped_over_array_containers
+    def mapped_func(x):
+        return func(x)
+
+    for ary in [ary_dof, ary_of_dofs, mat_of_dofs, dc_of_dofs]:
+        result = mapped_func(ary)
+        _check_allclose(func, ary, result)
+
+    @mapped_over_array_containers(leaf_class=DOFArray)
+    def check_leaf(x):
+        assert isinstance(x, DOFArray)
+
+    for ary in [ary_dof, ary_of_dofs, mat_of_dofs, dc_of_dofs]:
+        check_leaf(ary)
+
+    # }}}
+
+
 def test_container_multimap(actx_factory):
     actx = actx_factory()
     ary_dof, ary_of_dofs, mat_of_dofs, dc_of_dofs, bcast_dc_of_dofs = \
@@ -764,7 +817,19 @@ def test_container_multimap(actx_factory):
     # {{{ check
 
     def _check_allclose(f, arg1, arg2, atol=2.0e-14):
-        assert np.linalg.norm(actx.to_numpy(f(arg1) - arg2)) < atol
+        from arraycontext import NotAnArrayContainerError
+        try:
+            arg1_iterable = serialize_container(arg1)
+            arg2_iterable = serialize_container(arg2)
+        except NotAnArrayContainerError:
+            assert np.linalg.norm(actx.to_numpy(f(arg1) - arg2)) < atol
+        else:
+            arg1_subarrays = [
+                subarray for _, subarray in arg1_iterable]
+            arg2_subarrays = [
+                subarray for _, subarray in arg2_iterable]
+            for subarray1, subarray2 in zip(arg1_subarrays, arg2_subarrays):
+                _check_allclose(f, subarray1, subarray2)
 
     def func_all_scalar(x, y):
         return x + y
@@ -779,17 +844,30 @@ def func_multiple_scalar(a, subary1, b, subary2):
     result = rec_multimap_array_container(func_all_scalar, 1, 2)
     assert result == 3
 
-    from functools import partial
     for ary in [ary_dof, ary_of_dofs, mat_of_dofs, dc_of_dofs]:
         result = rec_multimap_array_container(func_first_scalar, 1, ary)
-        rec_multimap_array_container(
-                partial(_check_allclose, lambda x: 1 + x),
-                ary, result)
+        _check_allclose(lambda x: 1 + x, ary, result)
 
         result = rec_multimap_array_container(func_multiple_scalar, 2, ary, 2, ary)
-        rec_multimap_array_container(
-                partial(_check_allclose, lambda x: 4 * x),
-                ary, result)
+        _check_allclose(lambda x: 4 * x, ary, result)
+
+    from arraycontext import multimapped_over_array_containers
+
+    @multimapped_over_array_containers
+    def mapped_func(a, subary1, b, subary2):
+        return func_multiple_scalar(a, subary1, b, subary2)
+
+    for ary in [ary_dof, ary_of_dofs, mat_of_dofs, dc_of_dofs]:
+        result = mapped_func(2, ary, 2, ary)
+        _check_allclose(lambda x: 4 * x, ary, result)
+
+    @multimapped_over_array_containers(leaf_class=DOFArray)
+    def check_leaf(a, subary1, b, subary2):
+        assert isinstance(subary1, DOFArray)
+        assert isinstance(subary2, DOFArray)
+
+    for ary in [ary_dof, ary_of_dofs, mat_of_dofs, dc_of_dofs]:
+        check_leaf(2, ary, 2, ary)
 
     with pytest.raises(AssertionError):
         rec_multimap_array_container(func_multiple_scalar, 2, ary_dof, 2, dc_of_dofs)